Question

6. For what values of k, the equation 9x2 + 6kx + 4 = 0 has equal roots?​

Answer 1

Answer:

For a quadratic equation having equal roots, the value of discriminant is equal to zero.

General Form of Quadratic Equation: ax² + bx + c = 0

Value of discriminant = b² - 4ac

where,

• 'b' is the coefficient of 'x'
• 'a' is the coefficient of 'x²'
• 'c' is the constant.

According to the question, the given equation is:

• 9x² + 6kx + 4 = 0

Calculating the discriminant we get:

⇒ (6k)² - 4 ( 9 ) ( 4 ) = 0

⇒ 36 k² = 36 ( 4 )

⇒ k² = 4

⇒ k = ± 2

Hence the value of 'k' can be either +2 (or) -2.

Answer 2

${\large{\bold{\rm{\underline{Question}}}}}$

★ For what values of k, the equation 9x² + 6kx + 4 = 0 has equal roots?

${\large{\bold{\rm{\underline{Given \; that}}}}}$

★ The equation 9x² + 6kx + 4 = 0 has equal roots

${\large{\bold{\rm{\underline{To \; find}}}}}$

★ The value of k.

${\large{\bold{\rm{\underline{Solution}}}}}$

★ The value of k = 2

${\large{\bold{\rm{\underline{Knowledge \; required}}}}}$

★ The general form of quadratic equation is ax² + bx + c = 0

★ The value of the discriminant is b² - 4ac

${\large{\bold{\rm{\underline{Full \; Solution}}}}}$

~ Let us calculate discriminant..!

➝ 9x² + 6kx + 4 = 0

➝ (6k)² - 4(9)(4) = 0

➝ (36k)² = 4(36)

➝ k² = 4

➝ k = √4

➝ k = 2

• Henceforth, 2 is the value of k for the equation 9x² + 6kx + 4 = 0 has equal roots.

${\large{\bold{\rm{\underline{Extra \; knowledge}}}}}$

Knowledge about Quadratic equations -

★ Sum of zeros of any quadratic equation is given by ➝ α+β = -b/a

★ Product of zeros of any quadratic equation is given by ➝ αβ = c/a

★ A quadratic equation have 2 roots

★ ax² + bx + c = 0 is the general form of quadratic equation

★ The value of the discriminant is b² - 4ac