find the value of k for which 9x²+2kx+1=0 have equal roots
Answers
EXPLANATION.
Quadratic polynomial.
⇒ 9x² + 2kx + 1 = 0. have equal roots.
As we know that,
D = Discriminant Or b² - 4ac.
For real and equal roots : D = 0.
⇒ (2k)² - 4(9)(1) = 0.
⇒ 4k² - 36 = 0.
⇒ 4k² = 36.
⇒ k² = 9.
⇒ k = √9.
⇒ k = ± 3.
MORE INFORMATION.
Solution of inequation.
⇒ If a > 0.
(1) = |x| < a Or x² < a² ⇔ - a < x < a.
(2) = |x| > a Or x² > a² ⇔ - a ∪ x > a. Or R - [-a, a].
(3) = If α < β.
(x - α)(x - β) < 0 ⇔ α < x < β.
(x - α)(x - β) ≤ 0 ⇔ α ≤ x ≤ β.
(4) = If α < β.
(x - α)(x - β) > 0 ⇔ x < α ∪ x > β.
(x - α)(x - β) ≥ 0 ⇔ x ≤ α ∪ x ≥ β
Answer:
EXPLANATION.
Quadratic polynomial.
⇒ 9x² + 2kx + 1 = 0. have equal roots.
As we know that,
D = Discriminant Or b² - 4ac.
For real and equal roots : D = 0.
⇒ (2k)² - 4(9)(1) = 0.
⇒ 4k² - 36 = 0.
⇒ 4k² = 36.
⇒ k² = 9.
⇒ k = √9.
⇒ k = ± 3.
EXTRA INFORMATION.
Solution of inequation.
⇒ If a > 0.
(1) = |x| < a Or x² < a² ⇔ - a < x < a.
(2) = |x| > a Or x² > a² ⇔ - a ∪ x > a. Or R - [-a, a].
(3) = If α < β.
(x - α)(x - β) < 0 ⇔ α < x < β.
(x - α)(x - β) ≤ 0 ⇔ α ≤ x ≤ β.
(4) = If α < β.
(x - α)(x - β) > 0 ⇔ x < α ∪ x > β.
(x - α)(x - β) ≥ 0 ⇔ x ≤ α ∪ x ≥ β