Problem Solving (PS) | Re: If and are the roots of the equation 2x^2 2x 3 = 0, find the

Sum of the roots of a quadratic is given by -b/a
Product of the roots of a quadratic is given byc/a

\( 2x^2 – 2x – 3 =0\)

\( α + β =\frac{-(-2)}{2} =1\)
\( αβ =-\frac{3}{2} \)

\( α^5β^2 + α^2β^5 = (αβ)^2 (α^3 + β^3)\)

If I am short on time, I am going to mark option (A) here and move on. Why? I see 2 in the denominator in the product of the roots and cubes and squares in the required expression. Option (A) does look good.

\( (α^3 + β^3) = (α + β)(α^2 + β^2 -αβ)\) (AlgebraicIdentity)
\( (α^3 + β^3) = (α +β)[(α + β)^2 - 2αβ - αβ] \text{ (because } x^2 + y^2 = (x+y)^2 -2xy)\)
\( (α^3 + β^3) =\frac{11}{2}\)

[m] α^5β^2 + α^2β^5 =(\frac{-3}{2} )^2 *\frac{11}{2} =[fraction]
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Statistics : Posted by KarishmaB • on 22 Aug 2023, 01:30 • Replies 2 • Views 132

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