Question

If alpha beta are roots of x2 -x-12=0 then equation whose roots are 2alpha 2beta

Answer 1

Step-by-step explanation:

x²-x-12=0

sum of roots

$\alpha + \beta$

= -b/a

=1

product of roots

$\alpha \beta$

=c/a

= -12

quadratic equation whose roots are

$2\alpha \: and \: 2 \beta$

x²-2(alpha+beta)x+4alpha.beta

x²-2x-48

Answer 2

Hey mate here is your answer.......

$sum \: of \: zeroes = - \frac{b}{a} \\ \alpha + \beta = 1 \\ 2 \alpha + 2 \beta = 2( \alpha + \beta ) = 2 \\ product \: of \: zeroes = \frac{c}{a} \\ \alpha \beta = - 12 \\ 2 \alpha \times 2 \beta = 4 \alpha \beta = - 48$

quadratic equation =

${x}^{2} - ( \alpha + \beta )x + \alpha \beta \\ {x}^{2} - 2x - 48$

Hence, required quadratic equation is

${x}^{2} - 2x - 48$

HOPE IT HELP YOU ........^_^