Question

If the roots of the equation 6 $x^2$ -5x + k = 0 are in the ratio 2:3, then k

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Answer 1

The roots of the equation are in the ratio 2 : 3. Take the roots as 2α and 3α.

2α + 3α = $\frac{5}{6}$

⇒ 5α = $\frac{5}{6}$

α = $\frac{1}{6}$

2α × 3α = $\frac{k}{6}$

6 × ${\alpha }^2$ = $\frac{k}{6}$

⇒ k = 36 × ${\alpha }^2$

= 36 × ${\left(\frac{1}{6}\right)}^2$

= 1