Question

quadratic poynomial 4x^2+12x+9 has 0s as alpha and beta now form a quadratic polynomial whose 0s are alpha-1 and beta-1 ?

Answer 1

$HEYA \: \\ 4x {}^{2} + 12x + 9 = 0 \\ \\ 4x {}^{2} + 6x + 6x + 9 = 0 \\ \\ 2x(2x + 3) + 3(2x + 3) = 0 \\ \\ (2x + 3) = 0 \: \: or \: \: (2x + 3) = 0 \\ \\ x = - 3 \div 2 \: \: \: or \: \: \: x = - 3 \div 2 \\ here \: both \: roots \: are \: equal \: \\ \alpha = \beta = - 3 \div 2 \\ \\ required \: quadratic\: equation \: in \: y \: is \: \\ \\ y {}^{2} - ( - 5)y + ( - 3 \div 2 \: \: - 1) {}^{2} = 0 \\ \\ y {}^{2} + 5y + 25 \div 4 = 0$

Answer 2

here is your answer Mate.......

α and β = by factorisation of polynomial.. we get....picture...

we got. ..α=β= -3/2

then.. α-1 = -3/2 -2/2 = -5/2

then.. the polynomial will be.... 4x^2 +20x -25

HOPE it helps you...