Question

what is the value of k so the following equation has equal roots 2x²-(k-2)x+1=0

pls answer​

Answer 1

Step-by-step explanation:

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Questions & Answers

CBSE

Mathematics

Grade 10

Quadratic Equations

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Values of k for which the quadratic equation 2x2+kx+k=0 has equal roots

A. 4,8

B. 0,4

C. 4,-8

D. 0,8

Answer

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Hint: To solve this question we will use the quadratic formula method to solve the quadratic equation of the form ax2+bx+c=0. The quadratic formula is x=−b±b2−4ac−−−−−−−√2a . In this formula, the part under the square root is known as the discriminant and it is denoted as D. When we have value D=0 it implies that the equation has two real and equal roots. So we use this condition to get the desired answer.

Complete step by step answer:

We have been given a quadratic equation 2x2+kx+k=0 .

We have to find the value of k for the quadratic equation has equal roots.

Now, we know that the given equation is of the form ax2+bx+c=0 and to have equal roots the value of discriminant of an equation will be equal to zero.

So, we have given the question that equation 2x2+kx+k=0 has equal roots.

So, we have D=0

Now, we know that D=b2−4ac−−−−−−−√

Now, substituting the values we get

⇒b2−4ac−−−−−−−√=0⇒k2−4×2×k−−−−−−−−−−−√=0⇒k2−8×k−−−−−−−−√=0⇒k2−8k=0

Now, simplifying further we get

⇒k(k−8)=0

Or we can write k=0 and k−8=0

So, we get two values of k k=0 and k=8 .