What will be the value of k, if the zeroes of x2+kx+12 differ by 1 - Maths - Polynomials

Question

What will be the value of k, if the zeroes of
x2+kx+12 differ by 1?

Harleen Birdi · Accepted Answer

The given quadratic equation is $x^{2} + k x + 12$ .

Let two roots be α and α – 1 [ $∵$ Roots differ by 1, taking α > 1 ]

Sum of roots = –k

$\Rightarrow α + (α - 1) = - k \Rightarrow α = \frac{1 - k}{2}$

Product of roots = 12

$\Rightarrow α (α - 1) = 12 \Rightarrow - (\frac{1 - k}{2}) (\frac{k + 1}{2}) = 12 \Rightarrow \frac{- 1}{4} (1 - k^{2}) = 12 \Rightarrow 1 - k^{2} = - 48 \Rightarrow k^{2} = 49 \Rightarrow k = \pm 7$

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What will be the value of k, if the zeroes of x2+kx+12 differ by 1?

What will be the value of k, if the zeroes of x²+kx+12 differ by 1?