It is given that the difference between the zeros of 4x2 – 8kx + 9 is 4 and k 0. Then, k = ?

Question

It is given that the difference between the zeros of 4x2 – 8kx + 9 is 4 and k > 0. Then, k = ?

KollegeApply · Accepted Answer

bb($\frac{5}{2}$) Explanation: For 4x2 – 8kx + 9 = 0, the sum of roots = 2k and the product = $\frac{9}{4}$. The difference of the roots is `|$\alpha$ - $\beta$| = sqrt(($\alpha$ + $\beta$)^2 - 4$\alpha$$\beta$) = sqrt((2k)^2 - 4 xx ($\frac{9}{4}$)) = sqrt(4k^2 - 9) Set this equal to 4: sqrt(4k^2 - 9) = 4` $\Rightarrow$ 4k2 – 9 = 16 $\Rightarrow$ 4k2 = 16 + 9 $\Rightarrow$ 4k2 = 25 $\Rightarrow$ k^2 = $\frac{25}{4}$ $\Rightarrow$ k = $\pm$$\frac{5}{2}$ Given k > 0, so k = $\frac{5}{2}$.

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