if the roots of the polynomial (p)= 3x²-3x+13m-9 are inverse to each other then find tje value of m. About the author Remi
Answer: Quadratic polynomial. 3x^2 – 3x + 13m – 9 = 0. One root is inverse to other. As we know that, Let the one root be = a. Other root = 1/a. Products of the zeroes of the quadratic equation. aß = c/a. a(1/a) = 13m – 9/3. 1 = 13m – 9/3. 3 = 13m – 9. 3 +9 = 13m. 12 = 13m. m = 12/13 Reply
EXPLANATION. Quadratic polynomial. ⇒ 3x² – 3x + 13m – 9 = 0. One root is inverse to other. As we know that, Let the one root be = α. Other root = 1/α. Products of the zeroes of the quadratic equation. ⇒ αβ = c/a. ⇒ α(1/α) = 13m – 9/3. ⇒ 1 = 13m – 9/3. ⇒ 3 = 13m – 9. ⇒ 3 + 9 = 13m. ⇒ 12 = 13m. ⇒ m = 12/13. MORE INFORMATION. Nature of the factors of the quadratic expression. (1) = Real and different, if b² – 4ac > 0. (2) = Rational and different, if b² – 4ac is a perfect square. (3) = Real and equal, if b² – 4ac = 0. (4) = If D < 0 Roots are imaginary and unequal or complex conjugate. Reply
Answer:
Quadratic polynomial.
3x^2 – 3x + 13m – 9 = 0.
One root is inverse to other. As we know that,
Let the one root be = a.
Other root = 1/a.
Products of the zeroes of the quadratic equation.
aß = c/a.
a(1/a) = 13m – 9/3.
1 = 13m – 9/3.
3 = 13m – 9.
3 +9 = 13m.
12 = 13m.
m = 12/13
EXPLANATION.
Quadratic polynomial.
⇒ 3x² – 3x + 13m – 9 = 0.
One root is inverse to other.
As we know that,
Let the one root be = α.
Other root = 1/α.
Products of the zeroes of the quadratic equation.
⇒ αβ = c/a.
⇒ α(1/α) = 13m – 9/3.
⇒ 1 = 13m – 9/3.
⇒ 3 = 13m – 9.
⇒ 3 + 9 = 13m.
⇒ 12 = 13m.
⇒ m = 12/13.
MORE INFORMATION.
Nature of the factors of the quadratic expression.
(1) = Real and different, if b² – 4ac > 0.
(2) = Rational and different, if b² – 4ac is a perfect square.
(3) = Real and equal, if b² – 4ac = 0.
(4) = If D < 0 Roots are imaginary and unequal or complex conjugate.