Question

The equation px^2-17x+6=0 has two distinct roots, α and β.Also, α/1​−β/1​= 13/6

Find the value of p.
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Answer 1

Answer:

Given that the eqn has two real and distinct roots

So , b^2 - 4ac > 0 (positive)

17^2 - 4*P*6 > 0

289 - 24P > 0

289 > 24 P

289/24 > 24P/24

12.04 > P

:. P is less than 12.04

Answer 2

We can use either eqn. (\blueD1)(1)left parenthesis, start color #11accd, 1, end color #11accd, right parenthesis or eqn. (\maroonD2)(2)left parenthesis, start color #ca337c, 2, end color #ca337c, right parenthesis to find ppp.

Using eqn. (\maroonD{2})(2)left parenthesis, start color #ca337c, 2, end color #ca337c, right parenthesis, we get

\begin{aligned} \alpha\beta&=\dfrac{6}{p}\\\\ \dfrac{2}{5}\cdot3&=\dfrac{6}{p}\\\\ p&=5 \end{aligned}αβ52⋅3p=p6=p6=5