If alpha. And beta are the …

We have, Polynomial 25p2−15p+2 On comparing that, Ap2+Bp+C Then, A=25,B=−15,C=2 Given that, Sum of roots =α+β=A−B​ α+β=2515​ α+β=53​ Product of roots α.β=AC​ α.β=252​ Now, 2α1​and2β1​ Then, Sum of roots 2α1​+2β1​=4αβ2α+2β​ =24αβ(α+β)​ =2αβ(α+β)​=252×2​53​​=53​×425​=415​ 2α1​+2β1​=415​ Product of roots =2α1​×2β1​=4αβ1​=254×2​1​ =825​ So, the equation of polynomial is p2−(Sumofroots)p+productofroots ⇒p2−415​p+825​ ⇒88p2−30p+25​ Hence, this is the answer. Was this answer helpful? 131 2 SIMILAR QUESTIONS If α and β are the zeroes of the quadratic polynomial f(x)=2x2−5x+7, then find a quadratic polynomial whose zeroes are 2α+3β and 2α+3β. Hard View solution > If α and β are the zeros of the polynomial x2+4x+3, find the polynomial where zeros are 1+αβ​ and 1+βα​. We have, Polynomial 25p2−15p+2 On comparing that, Ap2+Bp+C Then, A=25,B=−15,C=2 Given that, Sum of roots =α+β=A−B​ α+β=2515​ α+β=53​ Product of roots α.β=AC​ α.β=252​ Now, 2α1​and2β1​ Then, Sum of roots 2α1​+2β1​=4αβ2α+2β​ =24αβ(α+β)​ =2αβ(α+β)​=252×2​53​​=53​×425​=415​ 2α1​+2β1​=415​ Product of roots =2α1​×2β1​=4αβ1​=254×2​1​ =825​ So, the equation of polynomial is p2−(Sumofroots)p+productofroots ⇒p2−415​p+825​ ⇒88p2−30p+25​ Hence, this is the answer. Was this answer helpful?

We have, Polynomial 25p 2 −15p+2 On comparing that, Ap 2 +Bp+C Then, A=25,B=−15,C=2 Given that, Sum of roots =α+β= A −B ​ α+β= 25 15 ​ α+β= 5 3 ​ Product of roots α.β= A C ​ α.β= 25 2 ​ Now, 2α 1 ​ and 2β 1 ​ Then, Sum of roots 2α 1 ​ + 2β 1 ​ = 4αβ 2α+2β ​ =2 4αβ (α+β) ​ = 2αβ (α+β) ​ = 25 2×2 ​ 5 3 ​ ​ = 5 3 ​ × 4 25 ​ = 4 15 ​ 2α 1 ​ + 2β 1 ​ = 4 15 ​ Product of roots = 2α 1 ​ × 2β 1 ​ = 4αβ 1 ​ = 25 4×2 ​ 1 ​ = 8 25 ​ So, the equation of polynomial is p 2 −(Sumofroots)p+productofroots ⇒p 2 − 4 15 ​ p+ 8 25 ​ ⇒ 8 8p 2 −30p+25 ​