If x=-3 and $x = \frac{2}{3}$ are solutions of quadratic equation $m x^{2} + 7 x + n = 0$ ,find the values of m and n.

Open in App

Solution

$m x^{2} + 7 x + n = 0$

Since x = -3 is a root,
$m (- 3)^{2} + 7 (- 3) + n = 0 \Rightarrow 9 m + n = 21 . . . (1)$

Since $x = \frac{2}{3}$ is a root,
$m {(\frac{2}{3})}^{2} + 7 (\frac{2}{3}) + n = 0 \Rightarrow \frac{4 m}{9} + \frac{14}{3} + n = 0 \Rightarrow 4 m + 9 n = - 42 . . . (2)$

Solving equations (1) and (2), we get m = 3 and n = -6

Suggest Corrections

Similar questions

If $x = \frac{2}{3}$ is a solution of the quadratic equation $7 x^{2} + m x - 3 = 0$ , find the value of m.

x = 2

x = - 3

a x^{2} + 7 x + b = 0

a

b

x = \frac{2}{3}

x = - 3

a x^{2} + 7 x + b = 0,

If $x = \frac{2}{3} a n d x = - 3$ are the roots of the quadratic equation $a x^{2} + 7 x + b = 0$ then find the values of a and b.

2

3

2 x^{3} + m x^{2} - 13 x + n = 0

m

n

Join BYJU'S Learning Program