Question

-4 is a root of equation x^2+px-4=0 and the equation has equal root find the value of p and q?​

Answer 1

Correct Question:

If - 4 is a root of the equation x² + px - 4 = 0 and the equation x² + px + q = 0 has equal root, find the values of p and q.

Answer:

The value of p is 3.

The value of q is 9 / 4.

Step-by-step-explanation:

The given quadratic equation is x² + px - 4 = 0.

We have given that,

The equation has real and equal roots with one root being - 4.

Now,

x² + px - 4 = 0

Comparing with ax² + bx + c = 0, we get,

• a = 1
• b = p
• c = - 4

Now,

- 4 is a root of the given equation.

∴ ( - 4 )² + p * ( - 4 ) - 4= 0

⇒ 16 - 4p - 4= 0

⇒ 12 - 4p = 0

⇒ 12 = 4p

⇒ p = 12 ÷ 4

⇒ p = 3

∴ The value of p is 3.

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Now,

The equation x² + px + q = 0 has equal roots.

Comparing with ax² + bx + c = 0,

• a = 1
• b = p = 3
• c = q

Now, we know that,

For real and equal roots, the value of discriminant is zero.

∴ b² - 4ac = 0

⇒ 3² - 4 * 1 * q = 0

⇒ 9 - 4q = 0

⇒ 9 = 4q

⇒ q = 9 / 4

∴ The value of q is 9 / 4.

Answer 2

Step-by-step explanation:

Given equation is

${x}^{2} + px - 4 \\ given \: \: \: \: \: \: \alpha = - 4 \\ \alpha + \beta = - p \\ - 4 + 1 = - p \\ p = 3 \\ \\ {p }^{2} - 4q = 0 \\ 9 - 4q = 0 \\ q = \frac{9}{4}$