Question

If both the zeros of a quadratic polynomelial x square +mx+9 are equal find the value of m​

Answer 1

P(x) = x² + mx + 9

• a = 1
• b = m
• c = 9

Let us first calculate the discriminant of the equation :

D = b² - 4ac

→ D = m² - 4 × 1 × 9

→ D = m² - 36

→ D + 36 = m²

For any quadratic equation to have equal roots , the value of discriminant must be equal to zero .

$\therefore$ 0 + 36 = m²

→ m² = 36

→ m= √36

→ m = 6

Let us calculate the zero of the equation :

$\tt x = \dfrac{ - b}{2a} \\ \\ \tt \implies x = \frac{ - 6}{2 \times 1} \\ \\ \tt \implies x = - 3$

Verification :

Substituting x = -3

P(-3) = (-3)² + 6 (-3) + 9

P(-3) = 9 - 18 + 9

P(-3) = 0

Hence , the value of x and m is -3 and 6 respectively.