Find the values of a and b for which x-3-4 and x-2 are the roots of equation ax2-bx-6-0

α +β = b/a⇒3/4 2= b/a⇒ 5/4= b/a αβ = c/a⇒3/4( 2)=c/a⇒ 6/4=c/a by comparing,we can all that,b = 5 amp; a = 4 ...

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Standard XII

Mathematics

Properties of Cube Root of a Complex Number

Find the valu...

Question

Find the values of $a$ and $b$ for which $x = \frac{3}{4}$ and $x = - 2$ are the roots of equation $a x^{2} + b x - 6 = 0$

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Solution

$α + β = \frac{- b}{a} \Rightarrow \frac{3}{4} - 2 = \frac{- b}{a} \Rightarrow \frac{- 5}{4} = \frac{- b}{a}$
$α β = \frac{c}{a} \Rightarrow \frac{3}{4} (- 2) = \frac{c}{a} \Rightarrow \frac{- 6}{4} = \frac{c}{a}$
by comparing,we can all that,
b = 5 & a = 4

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Find the values of a and b for which x=34 and x=−2 are the roots of equation ax2+bx−6=0

α+β=−ba⇒34−2=−ba⇒−54=−baαβ=ca⇒34(−2)=ca⇒−64=caby comparing,we can all that,b = 5 & a = 4

Find the values of $a$ and $b$ for which $x = \frac{3}{4}$ and $x = - 2$ are the roots of equation $a x^{2} + b x - 6 = 0$

$α + β = \frac{- b}{a} \Rightarrow \frac{3}{4} - 2 = \frac{- b}{a} \Rightarrow \frac{- 5}{4} = \frac{- b}{a}$
$α β = \frac{c}{a} \Rightarrow \frac{3}{4} (- 2) = \frac{c}{a} \Rightarrow \frac{- 6}{4} = \frac{c}{a}$
by comparing,we can all that,
b = 5 & a = 4