If - - are roots of the equation 4 - 2-3 x-7-0- then 1 - -1 - - is equal toa 7 - 3b -7 - 3c 3 - 7d -3 - 7

(d) minus;3/7 Given equation: nbsp;4x2 #160;+ #160;3x #160;+ #160;7 #160;= #160;0 Also, nbsp; #945; nbsp;and nbsp; #946; nbsp;are ...

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Standard XII

Mathematics

Inequalities Involving Mathematical Means

If α, β are r...

Question

If α, β are roots of the equation $4 x^{2} + 3 x + 7 = 0, then 1 / α + 1 / β$ is equal to
(a) 7/3
(b) −7/3
(c) 3/7
(d) −3/7

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Solution

(d) −3/7

Given equation: $4 x^{2} + 3 x + 7 = 0$
Also, $α$ and $β$ are the roots of the equation.

Sum of the roots = $α + β = \frac{- C oefficient of x}{C oefficient of x^{2}} = - \frac{3}{4}$

Product of the roots = $α β = \frac{C onstant term}{C oefficient of x^{2}} = \frac{7}{4}$

∴ $\frac{1}{α} + \frac{1}{β} = \frac{α + β}{α β} = \frac{- \frac{3}{4}}{\frac{7}{4}} = - \frac{3}{7}$

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If α, β are roots of the equation 4x2+3x+7=0, then 1/α+1/β is equal to (a) 7/3 (b) −7/3 (c) 3/7 (d) −3/7

(d) −3/7 Given equation: 4x2 + 3x + 7 = 0 Also, α and β are the roots of the equation. Sum of the roots = α + β =-Coefficient of xCoefficient of x2=-34 Product of the roots = αβ =Constant termCoefficient of x2= 74 ∴ 1α + 1β = α + βαβ = -3474 =-37

If α, β are roots of the equation $4 x^{2} + 3 x + 7 = 0, then 1 / α + 1 / β$ is equal to
(a) 7/3
(b) −7/3
(c) 3/7
(d) −3/7