Question

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Answer 1

★Given★

the roots of quadratic equation, given as:

p(x)=9x²+kx+49=0

are equal.

To Find

The value of 'k'

★Solution★

For equal roots of a quadratic equation, its discriminant needs to be zero.

, i.e., D=b²–4ac=0

OR b²=4ac .....(1st) eq.ⁿ

Now, In the given quadratic equation, i.e., p(x)=9x²+kx+49=0.

On comparing with its general formula, i.e., p(x)=ax²+bx+c=0

We get, a=9, b=k, and, c=49

Now, On substituting the above values of a, b and c in the (1st) eq.ⁿ, we get:

b²=4ac

» (k)²=(4)(9)(49)

» k²=36×49

» k²=(6)²×(7)²

OR k=√[(6)²×(7)²]

» k=6×7

(2)nd Option, i.e., k=42

Therefore, if the roots of the given polynomial are exactly equal, then the value of k is 42.