Question

solve for x x(2x+1)=6​

Answer 1

ANSWER.

• The values of x are -2 and 1.5.

SOLUTION.

Given,

→ x(2x + 1) = 6

→ 2x² + x - 6 = 0

By splitting the middle term, we get,

→ 2x² + 4x - 3x - 6 = 0

→ 2x(x + 2) - 3(x + 2) = 0

→ (2x - 3)(x + 2) = 0

By zero product rule,

→ (2x - 3) = 0 or (x + 2) = 0

→ x = 3/2, -2

★ So, the values of x are 1.5 and -2.

LEARN MORE.

⊕ General form of a quadratic equation -

→ ax² + bx + c = 0

Here,

→ a = Coefficient of x².

→ b = Coefficient of x.

→ c = Constant term.

⊕ How to solve?

To solve a quadratic equation, we have to split the middle term and then using zero-product rule, the roots are calculated.

⊕ Sum and product of roots.

1. Sum of roots of a quadratic equation = -b/a

2. Product of roots of a quadratic equation = c/a

⊕ Nature of roots.

∅ The discriminant of a quadratic equation tells us about the nature of roots.

Discriminant (D) = b² - 4ac.

1. If D > 0, roots are real and distinct.
2. If D = 0, roots are equal and real.
3. If D < 0, roots are imaginary.