Question

If $\alpha \beta$ are the zeros of the polynomial $f(x)= 4x^{2}+3x+7$, then $\frac{1}{\alpha} + \frac{1}{\beta}$ is equal to
(a) $\frac{7}{3}$
(b) $-\frac{7}{3}$
(c) $\frac{3}{7}$
(d) $-\frac{3}{7}$

Answer 1

SOLUTION :

The correct option is (d) : - 3/7.

Given : α  and β are the zeroes of the  polynomial p(x) = 4x² + 3x +7

On comparing with ax² + bx + c,

a = 4, b= 3, c = 7

Sum of the zeroes = −coefficient of x / coefficient of x²

α + β  = -b/a = - 3/4  

α + β  = - 3/4 ………………….(1)

Product of the zeroes = constant term/ Coefficient of x²

αβ = c/a = 7/4  

αβ = 7/4 ……………………(2)

The value of 1/α + 1/ β :

1/α + 1/ β = (α + β) /αβ

= - ¾ / 7/4

[From eq 1 & 2 ]

= - ¾ × 4/7 = - 3/7

1/α + 1/ β = - 3/7

Hence, the value of 1/α + 1/ β is - 3/7.

HOPE THIS ANSWER WILL HELP YOU…

Answer 2

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