Question

if the zero of quadratic polynomial is (k^2-14)x^2-2x-12is 1 then find the value of k​

Answer 1

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Given :-

• p(x) = (k^2 - 14) x^2 - 2x - 12
• Zero of the polynomial is 1

To Find :-

• The value of 'k'

Solution :-

If a is the zero of the polynomial, then p(a) = 0.

Then,

Here, a = 1, hence, p(1) = 0

Substituting the value as 1 :

$\sf{p(a) = ( {k}^{2} - 14) {x}^{2} - 2x - 12 } = 0\\ \sf{ ( {k}^{2} - 14) {1}^{2} - 2(1) - 12 = 0 } \\ \sf{ ( {k}^{2} - 14) - 2 - 12 = 0 } \\ \sf{ {k}^{2} - 28 = 0 } \\ \sf{k = \sqrt{28} } \\ \star \: \underline{\boxed{ \sf{k = \sqrt[2]{7} }}} \: \star$

@SweetestBitter