Question

If x=12 is one root of the quadratic equation x²-2kx-20=0 then find value ok k.​

Answer 1

Answer:

Let

p(x) = x²-2kx-20=0

x= 12 is one root of the quadratic equation

Remainder = p(12) = 0

=> p(12)=0

=> (12)²-2k(12) - 20 = 0

=> 144-24k-20=0

=> -24k=20-144

=> - 24k = -124

=> k=124/24

=> k=31/6

Answer 2

Answer:

By Vieta’s formulas, the sum of the roots is 63.

Now all primes are odd except 2, but 63 is odd, so one root is even and one root is odd. So one of the roots is 2, and the other is 61, which is indeed prime.

Finally, k is the product of roots = 2 x 61 = 122.

Step-by-step explanation: