Question

if the squared difference of the zeros of quadratic polynomial is f(x) equal to X square + kx + 45 is equal to 144 find the value of k

Answer 1

${x}^{2} + kx + 45 = 0 \\ \alpha + \beta = - k \\ \alpha \beta = 45 \\ given \\ {( \alpha - \beta) }^{2} = 144 \\ ( \alpha + \beta ) {}^{2} - 4 \alpha \beta = 144 \\ {k}^{2} - 4(45) = 144 \\ {k}^{2} = 144 + 180 \\ k {}^{2} = 324 \\ k = \sqrt{324}$
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