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# Find the Values Of K For Which the Roots Are Real and Equal in Each of the Following Equation: Kx2 + Kx + 1 = -4x2 - X - Mathematics

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#### Question

Find the values of k for which the roots are real and equal in each of the following equation:

kx2 + kx + 1 = -4x2 - x

#### Solution

The given quadric equation is kx2 + kx + 1 = -4x2 - x, and roots are real and equal

Then find the value of k.

Here,

kx2 + kx + 1 = -4x2 - x

4x2 + kx2 + kx + x + 1 = 0

(4 + k)x2 + (k + 1)x + 1 = 0

So,

a = (4 + k), b = (k + 1) and c = 1

As we know that D = b2 - 4ac

Putting the value of a = (4 + k), b = (k + 1) and c = 1

= (k + 1)2 - 4 x (4 + k) x (1)

= (k2 + 2k + 1) - 16 - 4k

= k2 - 2k - 15

The given equation will have real and equal roots, if D = 0

Thus,

k2 - 2k - 15 = 0

Now factorizing of the above equation

k2 - 2k - 15 = 0

k2 - 5k + 3k - 15 = 0

k(k - 5) + 3(k - 5) = 0

(k - 5)(k + 3) = 0

So, either

k - 5 = 0

k = 5

Or

k + 3 = 0

k = -3

Therefore, the value of k = 5, -3.

Is there an error in this question or solution?

#### APPEARS IN

RD Sharma Solution for Class 10 Maths (2018 (Latest))