Question

The value of p for equation 2x² – 4x + P = 0 to have real roots will beThe value of p for equation 2x² – 4x + P = 0 to have real roots will be​

Answer 1

Given :-

▪ A quadratic equation,

• 2x² - 4x + p = 0

To Find :-

▪ Value of p for which the given Quadratic equation will have real and equal roots.

Solution :-

This is related to the discriminant of a quadratic equation which is equal to b² - 4ac providing a quadratic equation as ax² + bx + c = 0

The discriminant of a quadratic equation tells us about the nature of roots whether they are real or imaginary or equal.

Comparing the given quadratic equation with the standard form of the quadratic equation i.e., ax² + bx + c = 0 , we have

• a = 2
• b = -4
• c = p

We have to find the value of p so that the quadratic equation will have equal roots, we know a quadratic equation will have real and equal roots only when its discriminant is equal to zero.

⇒ b² - 4ac = 0

⇒ (-4)² - 4×2×p = 0

⇒ 16 = 8p

⇒ p = 2

Hence, The value of p is 2.

Answer 2

Answer:

▶ P = 2

Explanation:

Given that,

▶Quadratic polynomial : 2x² - 4x + p = 0.

▶On comparing with given quadratic polynomial with ax² + bx + c = 0 : We get,

▶a = 2 , b = -4 , c = p

.°. Roots are real and equal,

▶ Δ = 0

▶ b² - 4ac = 0

▶ (-4)² - 4 × 2 × p = 0

▶ 16 - 8p = 0

▶ 16 = 8p

▶ p = 16/8

▶ p = 2

Hence,

• The value of p is 2.