Find the nature of roots
x2 + 2x - 9=0
Answers
EXPLANATION.
Quadratic equation.
⇒ x² + 2x - 9 = 0.
As we know that,
D = Discriminant Or b² - 4ac.
⇒ D = (2)² - 4(1)(-9).
⇒ D = 4 + 36.
⇒ D = 40.
Roots are real and different D > 0.
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.
Required solution...
It is given that we have to find out the nature of the root x² + 2x - 9 = 0.
We have to use the formula to find the discriminant. And the formula is b²-4ac.
Discriminant tell us about there are solution of a quadratic equation that are no solution, one solution and two solution.
→ Discriminant = b²-4ac.
- Here b is 2, a is 1 and c is 9.
→ (2)² - 4(1)(-9)
→ (2)² -4(-9)
→ (2)² +36
→ 4 + 36
→ 40
- Henceforth, the nature of the root are different and real that's because D is greater than 0.
Additional information:
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
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