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If the Sum and Product of the Roots of the Equation Kx2 + 6x + 4k = 0 Are Real, Then K = - CBSE Class 10 - Mathematics

ConceptSolutions of Quadratic Equations by Factorization

Question

If the sum and product of the roots of the equation kx2 + 6x + 4k = 0 are real, then k =

• $- \frac{3}{2}$

• $\frac{3}{2}$

• $\frac{2}{3}$

• $- \frac{2}{3}$

Solution

The given quadric equation is kx2 + 6x + 4k = 0, and roots are equal

Then find the value of c.

Let alpha and betabe two roots of given equation

And,  a = k,b = 6 and , c = 4k

Then, as we know that sum of the roots

alpha + beta = (-b)/a

alpha +beta = (-6)/a

And the product of the roots

alpha. beta = c/a

alpha beta = (4k)/k

= 4

According to question, sum of the roots = product of the roots

(-6)/k = 4

4k = -6

k = (-6)/4

= (-3)/2

Therefore, the value of c = (-3)/2.

Is there an error in this question or solution?

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Solution If the Sum and Product of the Roots of the Equation Kx2 + 6x + 4k = 0 Are Real, Then K = Concept: Solutions of Quadratic Equations by Factorization.
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