Find the value of k for which the two roots are real and equal. 4x square plus kx plus 9 = 0?

Question

Answer

Answer

The given Equation has two real and equal roots .

Hence , we can state that D = 0

=> B ^ 2 = 4 A C

Given Quadratic Equation :

4 X ^ 2 + K x + 9 = 0

=> B = K

=> B ^ 2 = K ^ 2

4 A C

=> 4 × 4 × 9

=> 144

=> K ^ 2 = 144

=> K = + 12 and - 12.

Hence two values of K, + 12 and - 12 satisfy the above Equation.

Answer

Answer

Introduction:
To find the value of k for which the given quadratic equation has real and equal roots, we need to determine the discriminant of the quadratic equation. The discriminant is the expression inside the square root in the quadratic formula and helps us determine the nature of the roots.

Quadratic Equation:
The given quadratic equation is 4x² + kx + 9 = 0.

Discriminant:
The discriminant (D) of a quadratic equation ax² + bx + c = 0 is given by the formula D = b² - 4ac.

In this case, a = 4, b = k, and c = 9. So, the discriminant is D = k² - 4(4)(9) = k² - 144.

Real and Equal Roots:
For a quadratic equation to have real and equal roots, the discriminant must be equal to zero (D = 0).

Finding the Value of k:
To find the value of k, we set the discriminant equal to zero and solve the equation k² - 144 = 0.

Calculating the Value of k:
To solve the equation k² - 144 = 0, we can factorize it as (k - 12)(k + 12) = 0.

Setting each factor equal to zero, we have two possible solutions:
k - 12 = 0 => k = 12
k + 12 = 0 => k = -12

Conclusion:
The value of k for which the given quadratic equation has real and equal roots is k = 12 or k = -12.

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