find the roots of this equation by factorisation
Answers
EXPLANATION.
Roots of the quadratic equations.
⇒ 2x² + x - 6 = 0.
As we know that,
Factorizes the equation into middle term splits, we get.
⇒ 2x² + 4x - 3x - 6 = 0.
⇒ 2x(x + 2) - 3(x + 2) = 0.
⇒ (2x - 3)(x + 2) = 0.
⇒ x = 3/2 and x = -2.
MORE INFORMATION.
Quadratic expression.
A polynomial of degree two of the form ax² + bx + c (a ≠ 0) is called a quadratic expression in x.
The quadratic equation.
ax² + bx + c = 0 (a ≠ 0) has two roots, given by.
⇒ α = - b + √D/2a.
⇒ β = - b - √D/2a.
D = Discriminant Or b² - 4ac.
Given that: A quadratic equation is given as 2x² + x - 6 = 0
To find: The root of the given quadratic equation by factorisation method.
Solution: The root of the given quadratic equation is 3/2 or -2
Using concept: Middle term splitting method.
Full Solution:
»»» 2x² + x - 6 = 0
»»» 2x² + 4x -3x -6 = 0
(∵ here two middle terms that are 4x and 3x. And whe we subtract them them we get x and when we into them then we get 12)
(∵ 2 × 6 = 12 and 4 × 3 = 12)
»»» 2x(x+2) - 3(x+2) = 0
»»» (x+2) (2x-3) = 0
~ Firstly,
- »» x = 0-2
- »» x = -2
~ Secondly,
- »» 2x = 0+3
- »» 2x = 3
- »» x = 3/2
Henceforth, x = 3/2 and -2.
Some 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
★ Discriminant is given by b²-4ac
- Discriminant tell us about there are solution of a quadratic equation as no solution, one solution and two solutions.
★ A quadratic equation have 2 roots
★ ax² + bx + c = 0 is the general form of quadratic equation
★ D > 0 then roots are real and distinct.
★ D = 0 then roots are real and equal.
★ D < 0 then roots are imaginary.
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