Question

(iii) what is the value of k for which the quadratic equation 3x2-kx+k=0has equal roots​

Answer 1

Answer:

for roots equal and real

b^2 _ 4ac =0

so a=3,b=K and c=3

k^2 _ 4×3×3=0

k^2 =0+36

k=under root 36

k=6

5.0

Answer 2

Question-

What is the value of k for which the quadratic equation 3x2-kx+k=0has equal roots​?

Answer-

k=6

Explanation-

The given quadratic equation is 3x^2 −2kx+12=0

On comparing it with the general quadratic equation ax^2+bx+c=0, we obtain  a=3,b=−2k and c=12.

Discriminant, ′ D ′ of the given quadratic equation is given by

D=b^2 −4ac

=(−2k) 2 −4×3×12

=4k 2 −144

For equal roots of the given quadratic equations, Discriminant will be equal to 0.

i.e., D=0

⇒4k^2 −144=0

⇒4(k^2−36)=0

⇒k^2 =36

⇒k=±6

Therefore, the values of k for which the quadratic equation 3x 2−2kx+12=0 will have equal roots are 6 and −6.

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