Question

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Answer 1

Required Answer:-

Given Equation:

• 2x² + 4√3x + p = 0

To find:

• The value of p for which the equation has equal roots.

Answer:

• The value of p is 6

Solution:

Given equation,

2x² + 4√3x + p = 0

Here,

a = 2

b = 4√3 and,

c = p

It's given that the roots of the quadratic equation are equal.

So, discriminant must be zero.

➡ b² - 4ac = 0

Substituting the values of a, b and c, we get,

➡ (4√3)² - 4 × 2 × p = 0

➡ 48 - 8p = 0

➡ 8p = 48

➡ p = 6

Hence, the value of p is 6 for which the roots of the given quadratic equation are equal.

At last, the equation will be ,

2x² + 4√3x + 6=0

Learn More:

Discriminant: It is the value obtained from a quadratic equation that tells the nature of the roots of the given quadratic equation. Roots may be real and unequal, equal or imaginary.

d = b² - 4ac

Where,

a = coefficient of x²

b = coefficient of x

c = coefficient of x^0

1. When d>0, roots are real and unequal.
2. When d=0, roots are equal and real.
3. When d<0, roots are imaginary.

Answer 2

Answer:

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