If α and β are the roots of the equation x2 - 4x + 5 = 0. then the quadratic equation whose roots are α2 + β and α + β2 is

Question

If α and β are the roots of the equation x2 - 4x + 5 = 0. then the quadratic equation whose roots are α2 + β and α + β2 is (A) x2 + 10x + 34 = 0 (B) x2 - 10x + 34 = 0 (C) x2 - 10x - 34 = 0 (D) x2 + 10x - 34 = 0

Tardigrade Admin · Accepted Answer

Since, α and β are roots of the quadratic equation x2-4 x+5=0 So, α+β=4 and α β=5 ... (i) Now, (α2+β)+(α+β2)=(α2+β2)+(α+β) =(α+β)2-2 α β+(α+β) =16-10+4=10 and (α2+β)(α+β2)=α3+α2 β2+β α+β3 =α3+β3+α β(α β+1) =(α+β)(α2+β2-α β)+α β(α β+1) =(α+β)[(α+β)2-3 α β]+α β(α β+1) =4[16-15]+5(5+1) =4+30=34 So, the quadratic equation whose roots are (α2+β) text and (α+β2) is x2-(α2+β+α+β2) x+(α2+β)(α+β2)=0 ⇒ x2-10 x+34=0

Q. If $α$ and $β$ are the roots of the equation $x^{2} - 4 x + 5 = 0$ . then the quadratic equation whose roots are $α^{2} + β$ and $α + β^{2}$ is

$x^{2} + 10 x + 34 = 0$

$x^{2} - 10 x + 34 = 0$

$x^{2} - 10 x - 34 = 0$

$x^{2} + 10 x - 34 = 0$

Q. If α and β are the roots of the equation x2−4x+5=0. then the quadratic equation whose roots are α2+β and α+β2 is

x2+10x+34=0

x2−10x+34=0

x2−10x−34=0

x2+10x−34=0

Q. If $α$ and $β$ are the roots of the equation $x^{2} - 4 x + 5 = 0$ . then the quadratic equation whose roots are $α^{2} + β$ and $α + β^{2}$ is

$x^{2} + 10 x + 34 = 0$

$x^{2} - 10 x + 34 = 0$

$x^{2} - 10 x - 34 = 0$

$x^{2} + 10 x - 34 = 0$