Question

Form a quadratic equation whose roots are  -3  and - 7 ​

Answer 1

Answer:

Quadratic Equation is

${x}^{2} + 10x + 21 = 0$

Step-by-step explanation:

Roots of the equations are

$\alpha = - 3 \: and \: \beta = - 7 \\ now \\ \alpha + \beta = - 3 + ( - 7) = - 10 \\ \alpha \beta = - 3 \times - 7 = 21$

Quadratic Equation is

${x}^{2} - ( \alpha + \beta )x + \alpha \beta = 0 \\ {x}^{2} - ( - 10)x + 21 = 0 \\ {x}^{2} + 10x + 21 = 0$

Other way

We have the roots

x=-3 and x =-7

We can write it as below

$(x + 3)(x + 7) = 0 \\ {x}^{2} + 7x + 3x + 21 = 0 \\ {x}^{2} + 10x + 21 = 0$