If x = −2 is a root of 3x² + kx − 2 = 0, find k.

Question

Accepted Answer

k = 5. A root satisfies the equation, so put x = −2 in: 3(−2)² + k(−2) − 2 = 0 → 12 − 2k − 2 = 0 → 2k = 10 → k = 5. Check: 3x² + 5x − 2 at x = −2 gives 12 − 10 − 2 = 0. Answer −5 comes from solving −2k = −10 with a sign slip; 7 and −7 come from writing 12 + 2 instead of 12 − 2 when collecting the constants.

If $x = - 2$ is a root of $3 x^{2} + k x - 2 = 0$ , find $k$ .

Step-by-Step Solution

Key idea: The discriminant — nature of roots

Master this chapter in 30 minutes a day.

More Class 10 Quadratic Equations practice

If x=−2 is a root of 3x2+kx−2=0, find k.

Step-by-Step Solution

Key idea: The discriminant — nature of roots

Master this chapter in 30 minutes a day.

More Class 10 Quadratic Equations practice

If $x = - 2$ is a root of $3 x^{2} + k x - 2 = 0$ , find $k$ .