Question

3 is a root of the quadratic equation x 2 - px + 6 = 0 and the quadratic equation px 2 - px - k = 0 has equal roots, then the values of p and k are:

Answer 1

Answer:

${x}^{2} - px + 6 = 0 \: \: has \: one \: root \: 3.$

$\alpha \beta = 6$

$\beta = \frac{6}{ \alpha } = \frac{6}{3} = 2$

$so \: \alpha + \beta = p = 3 + 2 = 5$

now 2nd eq.

$p {x}^{2} - px - k = 0 \: \: has \: equal \: roots \: then \:$

Discriminant = 0

i.e

$( - p) {}^{2} - 4p( - k) = 0$

putting P = 5

$25 + 20k = 0$

$k = - \frac{25}{20} = - \frac{5}{4}$

so

$p = 5 \: \: and \: \: k = - \frac{5}{4}$

Ans.

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Mark BRAINLIEST if this is helpful to you. Thanks