Question

Without solving the following quadratic equation, find the value of ‘p’ for which the

roots are equal : px2 + 8x – 3 = 0​

Answer 1

Answer:

The value of p is - 16 / 3.

Step-by-step-explanation:

The given quadratic equation is px² + 8x - 3 = 0.

We have to find the value of p.

Comparing the given equation with ax² + bx + c = 0, we get,

• a = p
• b = 8
• c = - 3

We have given that,

The quadratic equation has real and equal roots.

For real and equal roots,

b² - 4ac = 0

⇒ 8² - 4 * p * ( - 3 ) = 0

⇒ 64 + 12p = 0

⇒ 4 ( 16 + 3p ) = 0

⇒ 3p + 16 = 0

⇒ 3p = - 16

⇒ p = - 16 / 3

∴ The value of p is - 16 / 3.

Answer 2

Question :-

Without solving the following quadratic equation, find the value of ‘p’ for which the roots are equal : px2 + 8x – 3 = 0.

Solution :-

Given :

• px² + 8x - 3 = 0

Need to find :

• p

Here, we have a Quadratic equation which is px² + 8x - 3 = 0. we use the formula for roots are equal.

Formula :

• b² - 4ac

But first we compare the Quadratic equation with ax² + bx + c = 0

On comparing we get,

• a = p
• b = 8
• c = -3

Now, on using formula we get,

$\rm:\longmapsto{(8) {}^{2} - 4(p)( - 3) }$

$\rm:\longmapsto{64 + 12p = 0} \\ \\ \rm:\longmapsto{12p = - 64} \: \: \: \\ \\ \rm:\longmapsto{p = \frac{ - 64}{12} } \: \: \: \: \: \: \\ \\ \bf:\longmapsto \red{p = \frac{ - 16}{3} } \: \: \:$

Answer :

• $\rm{p = \frac{ - 16}{3} }$

Additional Information :-

Nature of roots :-

Let us consider a quadratic equation ax² + bx + c = 0, then nature of roots of quadratic equation depends upon Discriminant (D) of the quadratic equation.

If Discriminant, D > 0, then roots of the equation are real and unequal.

If Discriminant, D = 0, then roots of the equation are real and equal.

If Discriminant, D < 0, then roots of the equation are unreal or complex or imaginary.

Where,

Discriminant, D = b² - 4ac

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