find the value of K for which the given equation has equal roots (k-12) x^2+2(k-12)x+2=0
Question
find the value of K for which the given equation has equal roots (k-12) x^2+2(k-12)x+2=0
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Mathematics
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2021-07-17T15:58:50+00:00
2021-07-17T15:58:50+00:00 1 Answers
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Answer:
The values of k for which the given equation has equal roots are 14 and 12.
Step-by-step explanation:
Given polynomial is;
(k-12) x^2+2(k-12)x+2=0;
here, a = (k-12);
b = -2(k-12);
c = 2
For equal roots, we know a discriminant and that is;
b² – 4ac = 0;
Thus , (-2(k-12))² – 4(k-12)(2) = 0;
4(k-12)²- 4(k-12)(2) = 0;
First value of k will be;
4(k-12){(k-12) – 2} = 0;
(k-12) – 2 = 0 / 4(k-12);
k – 12 – 2 = 0;
k – 14= 0;
k = 14.
Second value of k will be;
4(k-12){(k-12) – 2} = 0;
4(k-12){(k-12) – 2} = 0 / {(k-12) – 2};
4(k-12) = 0;
k – 12= 0;
k = 12.
That’s all.