Question

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If one root of the equation
${x}^{2} + px + 12 = 0$ is 4 , write the equation
$x^{2} + px + q = 0$ has equal roots then the value of q is ​

Answer 1

Question :

If one root of the equation

$\sf{x}^{2} + px + 12 = 0$ is 4 , write the equation

$\sf x^{2} + px + q = 0$ has equal roots then the value of q is

Solution :

4 is the square root of x² + px + 12 = 0

⟹ p = -7

Equation of x² + px + q = 0 has equal roots

Discriminant = b² - 4ac

(Discriminant = 0 when roots of a quadratic equations are equal)

D = (-7)² - 4 × 1 × q = 0

⟹ q = 49/4

Answer 2

Question :

If one root of the equation

\sf{x}^{2} + px + 12 = 0x

2

+px+12=0 is 4 , write the equation

\sf x^{2} + px + q = 0x

2

+px+q=0 has equal roots then the value of q is

Solution :

4 is the square root of x² + px + 12 = 0

⟹ p = -7

Equation of x² + px + q = 0 has equal roots

Discriminant = b² - 4ac

(Discriminant = 0 when roots of a quadratic equations are equal)

D = (-7)² - 4 × 1 × q = 0

⟹ q = 49/4