find the value of the k,so they have two equal root 3x2 +kx+6=0
Answers
EXPLANATION.
Value of k, if equation has equal roots,
p(x) = 3x² + kx + 6 = 0.
As we know that,
For real and equal roots,
⇒ D = 0 Or b² - 4ac = 0.
⇒ (k)² - 4(3)(6) = 0.
⇒ k² - 72 = 0.
⇒ k² = 72.
⇒ k = √72.
⇒ k = 6√2.
MORE INFORMATION.
Maximum & Minimum value of quadratic expression,
In a quadratic expression ax² + bx + c.
(1) = If a > 0, quadratic expression has least value at x = -b/2a. This least value is given by 4ac - b²/4a = -D/4a.
(2) = If a < 0, quadratic expression has greatest value at x = -b/2a. This greatest value is given by 4ac - b²/4a = -D/4a.
★ Find the value of the k so they have two equal root 3x² + kx + 6 = 0.
★ Quadratic equation = 3x² + kx + 6 = 0 having same / equal roots.
★ Value of k.
★ Value of k = 6√2
★ As it's given that the roots are equal here so we have to use dimension for real and equal roots.
★ b² - 4ac = 0
✨ b is k so, b² is k²
✨ a is 3
✨ c is 6
~ So according to the rule let's put the values,
➝ b² - 4ac = 0
➝ k² - 4(3)(6) = 0
➝ k² - 4 × 3 × 6 = 0
➝ k² - 4 × 18 = 0
➝ k² -72 = 0
➝ k² = 0 + 72
➝ k² = 72
➝ k = √72
- Final value,
➝ k = 6√2
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