Question

Without solving the following quadratic equation,
find the value of p for which the roots are equal.
px² - 4x +3=0

Answer 1

Answer:

4/3

Step-by-step explanation:

If the roots of this quadratic equation are equal-

then, b^2-4ac=0

then,

The general form of a quadratic equation is ax^2+bx+c=0

here,

a=p

b=-4 and

c=3

then

b^2-4ac=0

=》-4^2-(4×p×3)=0

=》16-12p=0

=》16=12p

=》12p=16

=》p=16/12

=》4/3

Hence,p=4/3

Answer 2

Answer:

• p = 4/3

Step-by-step explanation:

Given

• px² - 4x + 3 = 0

To find

• Value of p for which the roots are real and equal.

Solution

px² - 4x + 3 = 0

Comparing to ax²+ bx + c = 0

We get:

• a = p
• b = -4
• c = 3

∴ Discriminant (D) = b² - 4ac

• -4² - 4 × p × 3
• 16 - 12p

For the equation to have real and equal roots, we must have D = 0

So:

• D = 0 = 16 - 12p = 0
• 12p = 16
• p = 16/12
• p = 4/3

∴ p = 4/3