If roots of equation 2x(square)+3x+4=0 are alpha and beta, then fine the quadratic equation whose roots are (alpha)square and (beta)square!

p.s.> sorry cudn't write in superscript

Question

If roots of equation 2x(square)+3x+4=0 are alpha and beta, then
fine the quadratic equation whose roots are (alpha)square and
(beta)square!

p s > sorry cudn't write in superscript

Ankush Jain · Accepted Answer

Given equation is :

$2 x^{2} + 3 x + 4 = 0 So, sum of roots = α + β = \frac{- 3}{2} and Product of roots = α β = \frac{4}{2} = 2$

Now, we have to find the quadratic equation whose roots are α² and β².

$∴ Sum of roots = α^{2} + β^{2} = {(α + β)}^{2} - 2 α β = (\frac{- 3}{2})^{2} - 2 (2) = \frac{9}{4} - 4 = \frac{9 - 16}{4} = \frac{- 7}{4} and product of roots = α^{2} β^{2} = {(α β)}^{2} = {(2)}^{2} = 4$

So, the quadratic equation = x² – (sum of roots)x + Product of roots

$= x^{2} - (\frac{- 7}{4}) x + 4 = x^{2} + \frac{7}{4} x + 4$

2

If roots of equation 2x(square)+3x+4=0 are alpha and beta, then fine the quadratic equation whose roots are (alpha)square and (beta)square! p.s.> sorry cudn't write in superscript

If roots of equation 2x(square)+3x+4=0 are alpha and beta, then fine the quadratic equation whose roots are (alpha)square and (beta)square!

p.s.> sorry cudn't write in superscript