Question

if alfha, beta are the zeros of f(x) = px^ - 2x +3p and alpha + beta =alphabeta then the value of p is:
a) 1/3
b)-2/3
c)2/3
d)-1/3​

Answer 1

Answer:-

Your Answer Is $\bf\dfrac{2}{3}.$

Explanation:-

Given:-

• A polynomial $\tt px^2-2x+3p.$

• $\tt\alpha$ And $\tt\beta$ are zerpes of the polynomial.

• $\tt\alpha+\beta = \alpha\: \beta$.

To Find:-

• The Value of p.

Concept Used:-

In a quadratic polynomial p(x) = ax²+bx+c if α and β are zeroes of the polynomial then,

$\\ \tt\mapsto\alpha + \beta = -\dfrac{b}{a}.$

$\\ \tt\mapsto\alpha\beta = \dfrac{c}{a}.$

Solution:-

So Here,

• a = p.
• b = -2.
• c = 3.

Therefore,

$\\ \tt\mapsto\alpha +\beta = -\dfrac{(-2)}{p}.$

$\\ \bf\mapsto\alpha+\beta = \dfrac{2}{p}---eq(1).$

Also,

$\\ \tt\mapsto\alpha\: \beta = \dfrac{3\cancel{p}}{\cancel{p}}.$

$\\ \bf\mapsto\alpha \beta = 3---eq(2).$

Also Acc To Que, eq(1) = eq(2),

$\\ \tt\mapsto\alpha +\beta = \alpha\beta.$

$\\ \tt\mapsto\dfrac{2}{p} = 3.$

$\\ \tt\mapsto 3p = 2.$

$\\ \large{\mapsto{\boxed{\bf p = \dfrac{2}{3}.}}}$

Therefore The Required Value Of p is $\bf\dfrac{2}{3}.$

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Answer 2

Answer:

c)2/3

hope my answer will help you