Question

If 2x^
2
- 8x + q = 0 has real and equal roots then the value of q is​

Answer 1

EXPLANATION.

if 2x² - 8x + q = 0 has real and equal roots,

To find the value of q is,

For real roots, D = 0  Or b² - 4ac = 0.

⇒ ( -8)² - 4(2)(q) = 0.

⇒ 64 - 8q = 0.

⇒ 64 = 8q.

⇒ q = 64/8.

⇒ q = 8.

The value of q = 8.

                             

MORE INFORMATION.

Higher degree equations.

The equation f(x) = a₀xⁿ + a₁xⁿ⁻¹ + ..... + aₙ₋₁x + aₙ = 0.   ........(1).

where the coefficient a₀ , a₁ , .....aₙ ∈ C and a₀ ≠ 0 is called an equation of Nth degree, which has exactly n roots a₁ , a₂ ...aₙ ∈ C then we can write,

p(x) = a₀( x - a₁)(x - a₂)......(x - aₙ) = a₀{ xⁿ - ( ∑a₁)xⁿ⁻¹ + (∑a₁a₂)xⁿ⁻² - .......+ ( -1)ⁿa₁a₂ .....aₙ }  ........(2).

compare equation (1) and (2) we get,

⇒ ∑a₁ = a₁ + a₂ +.....+aₙ = -a₁/a₀

⇒ ∑a₁a₂ = a₁a₂ +.....+aₙ₋₁aₙ = a₂/a₀

⇒ a₁a₂.....aₙ = (-1)ⁿaₙ/a₀

Answer 2

Answer:

Given :-

• 2x² - 8x + q = 0 has real and equal roots.

To Find :-

• What is the value of q.

Solution :-

Given equation : x² - 8x + q = 0

where, a = 2, b = - 8, c = q

Since, the two roots are real and equal.

➤ Discriminant = 0

➙ b² - 4ac = 0

Put, a = 2, b = - 8, c = q we get,

↦ (- 8)² - 4 × 2 × q = 0

↦ (- 8) × (- 8) - 8q = 0

↦ 64 - 8q = 0

↦ 64 = 8q

↦ 64 ÷ 8 = q

↦ 8 = q

➠ q = 8

∴ The value of q is 8 .

★ Extra Information ★

As we know that,

» b² - 4ac of the quadratic equation ax² + bx + c [where, a, b, c are real numbers and a ≠ 0] determines the nature of the roots, b² - 4ac is called the Discriminant of that quadratic equation.

➦ The two roots of the qradratic equation is ax² + bx + c = 0 [a ≠ 0]

➙ Real and equal if b² - 4ac

➙ Real and unequal if b² - 4ac > 0

➙ No real roots if b² - 4ac < 0