If the discriminant is 0, the equation has a real solution, a double root. We can further classify real solutions as rational or irrational.If the discriminant is Perfect square, the root is rational, the equation factorizes.

What if the quadratic equation is a perfect square?

When a polynomial is multiplied by itself, it is a perfect square.Example – The polynomial ax2 + bx + c is a perfect square if b2 = 4ac.

What is Radican in quadratic formula?

More about quadratic equations Discriminant: The radicand of the quadratic formula b2-4ac (the expression under the square root) is called the discriminant. By determining the value of the discriminant, the properties (quantity and type) of the solution can be calculated.

When the discriminant is a perfect square?

If the discriminant is a perfect square, then The solution of the equation is not only real, but also rational. If the discriminant is positive but not a perfect square, the solution to the equation is real but unreasonable. Determine the properties of the solutions to each quadratic equation.

What if there is no square root in the quadratic formula?

Anytime you end up with a zero within the square root of a quadratic formula, you will only get a solution to the equationin the sense of getting a number to solve the equation.

Simplified root expression (quadratic form)

26 related questions found

Does a have to be positive in a quadratic formula?

It has the general form: 0 = ax2 + bx + c each The number of constant terms (a, b, and c) can be positive or negative. Quadratic equations can always be solved by using the quadratic formula: … Since nothing can exist as a negative concentration, the other answer must be correct.

Is 4 a perfect square?

4 is a perfect square. A perfect square is a value with an integer square root. The square root of 4 is 2, so its square root is an integer, which means 4 is a perfect square. Another example of a perfect square is 9.

What if the discriminant is zero?

The discriminant is zero Quadratic has a repeated real solution. A negative discriminant means that neither solution is real.

What is the square root of 100?

The square root of 100 is 10. It is a positive solution to the equation x2 = 100. The number 100 is a perfect square.

What is the discriminant equal to?

The discriminant is the formula b square minus 4ac Remember that a, b, and c are quadratic coefficients in standard form. It tells you the number of solutions to the quadratic equation. If the discriminant is greater than zero, there are two solutions.

How many solutions does the quadratic formula have?

As we can see, there are Can be 0, 1 or 2 solutions Quadratic equation, depending on whether the expression in the square root sign (b2 – 4ac) is positive, negative, or zero. This expression has a special name: discriminant.

Is 25 a perfect square?

25 is a perfect square. 25 is a natural number, because there is another natural number 5, so 52 = 25, so 25 is a perfect square. Since 25 is a natural number and the square root of 25 is a natural number (5), 25 is a perfect square. 102.01 is a perfect square.

How do you prove that an equation is a perfect square?

In an equation of the form a²x²+2abx+b² = 0, the expression on the left can be decomposed as (ax+b)². The concept of a perfect square is the key to completing the square.

What happens when B 2 4ac 0?

If (b2 – 4ac) > 0.0, there are two real roots (that is, the equation crosses the x-axis in two places—the x-intercept). the root of a negative number).If (b2-4ac) = 0, then Only one real root exists – the parabola touches the x-axis at one point.

What if the discriminant is negative?

If the discriminant is negative, it means that there is Negative numbers under square root in quadratic formula. You may have learned in the past that you « can’t take the square root of a negative number ». The fact is that you can take the square root of a negative number, but the answer isn’t true.

What are the real and different roots?

If an equation has real roots, then the solution or root of the equation belongs to the set of real numbers.If the equations have different roots, then we say All solutions or roots of the equation are not equal. When the discriminant of a quadratic equation is greater than 0, it has real and distinct roots.

Is 17 a perfect square?

Is size 17 a perfect square? The number 17 is a prime number. This means that the square root of 17 cannot be represented as the product of two equal integers. so, The number 17 is not a perfect square.

Is 90 a perfect square?

90 is not a perfect square, however, it is a semi-perfect number, which means it is the sum of all or some of the divisors. The square root of 90 is half the power of 90.

Is 75 a perfect square?

we just 75 times 3 Make it a perfect square. This is because, 75 = 5 × 5 × 3. 3 does not have a pair. So 75 × 3 = 225 and √225 is 15.

What are the rules for quadratic equations?

generalize

• Quadratic equation in standard form: ax2 + bx + c = 0.
• Quadratic equations can be decomposed.
• Quadratic formula: x = −b ± √(b2 − 4ac) 2a.
• When the discriminant (b2−4ac) is: positive, there are 2 real solutions. Zero, there is a real solution. No, there are 2 complicated solutions.

What is a secondary example?

Examples of other forms of quadratic equations include: x(x – 2) = 4 [upon multiplying and moving the 4, becomes x² – 2x – 4 = 0] x(2x + 3) = 12 [upon multiplying and moving the 12, becomes 2x² – 3x – 12 = 0] 3x(x + 8) = -2 [upon multiplying and moving the -2, becomes 3x² + 24x + 2 = 0]