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# If the Sum of the Roots of the Equation X 2 − ( K + 6 ) X + 2 ( 2 K − 1 ) = 0 is Equal to Half of Their Product, Then K = - CBSE Class 10 - Mathematics

ConceptSolutions of Quadratic Equations by Factorization

#### Question

If the sum of the roots of the equation $x^2 - \left( k + 6 \right)x + 2\left( 2k - 1 \right) = 0$ is equal to half of their product, then k =

• 6

• 7

• 1

• 5

#### Solution

The given quadric equation is x^2 - (k+6)x + 2 (2k - 1) = 0 , and roots are equal

Then find the value of k.

Let alpha and beta  be two roots of given equation

And, a = 1, b = -(k + 6) and , c = 2 (2k - 1)

Then, as we know that sum of the roots

alpha + beta = (-b)/a

alpha + beta = (-{-(k + 6)})/1

= (k + 6)

And the product of the roots

alpha . beta = c /a

alphabeta = (2(2k - 1))/1

 = 2 (2k- 1)

According to question, sum of the roots  = 1/2 xx product of the roots

(k + 6) = 1/2 xx 2 (2k - 1)

k+6 = 2k - 1

 6+1 = 2k - k

7 = k

Therefore, the value of k = 7.

Is there an error in this question or solution?

#### APPEARS IN

Solution If the Sum of the Roots of the Equation X 2 − ( K + 6 ) X + 2 ( 2 K − 1 ) = 0 is Equal to Half of Their Product, Then K = Concept: Solutions of Quadratic Equations by Factorization.
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