Question

obtain the qudratic equatio if roots are -3 & -7​

Answer 1

x²+10x+21=0

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Answer 2

Given :

• Roots of quadratic equation = -3 and -7

To find :

• qudratic equation whose roots are -3 and -7

Concept used :

General form of quadratic equation :-

$\sf x^{2} - (sum \: of \: roots)x + (Products \: of \: roots) = 0$

Solution :

Roots of quadratic equation = -3 and -7

$\implies\sf Sum \: of \: roots = -3 + (-7)$

$\implies\sf Sum \: of \: roots = -3 -7$

$\implies\sf Sum \: of \: roots = - 10$

Now we will find product of roots :-

$\sf\implies product \: of \: roots = (-3) \times (-7)$

$\sf\implies product \: of \: roots = 21$

Quadratic equation whose roots are -3 and -7 :-

$\sf \implies x^{2} - ( - 10)x + (21) = 0$

$\sf \implies x^{2} + 10x + 21= 0$

Answer :

$\sf\large x^{2} + 10x + 21= 0$