Question

Q.3.
Find the values of p for which the quadratic equation has equal roots.
4x2 + px + 3 = 0

Answer 1

Answer:

4x2 + px + 3 = 0

Equation has equal roots,

∴ D = 0,

b²-4ac = 0

after comparison ax²+bx+c=0

a= 4, b= p & c= 3

∴ p²-4(4)(3) = 0

p² = 48

p = √48

p = ±4√3

Answer 2

Given:-

4x² + px + 3 = 0

To Find:-

The value of p.

Solution:-

Since, the quadratic equation 4x² + px + 3 = 0 has equal roots.

So,

$\bf b² \: – \: 4ac \: = \: 0$

$\bf => \: p² \: – \: 4 \: × \: 4 \: × \: 3 \: = \: 0 \: [ \: Since, \: here \: \: a \: = \: 4, \: b \: = \: p \: and \: c \: = \: 3 \: ]$

$\bf => \: p² \: – \: 48 \: = \: 0$

$\bf => \: p² \: = \: 48$

$\bf => \: p \: = \: √48$

$\bf => \: p \: = \: ±4√3$

Hence, the value of p is ±4√3 [Ans]

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