The roots of the quadratic equation 2x2 - x - 6 = 0 are: 1. -2, 3/2 2. 2, -3/2 3. -2, -3/2 4. 2, 3/2

Given, ⇒ 2x2 - x - 6 = 0 ⇒ 2x2 - 4x + 3x - 6 = 0 ⇒ 2x(x - 2) + 3(x - 2) = 0 ⇒ (2x + 3)(x - 2) = 0 ⇒ 2x + 3 = 0 or x - 2 = 0 [Using Zero-product rule] ⇒ 2x = -3 or x = 2 ⇒ x = or x = 2 Hence, option 2 is the correct option.

Mathematics

The roots of the quadratic equation 2x² - x - 6 = 0 are:
-2, $\dfrac{3}{2}$
2, $\dfrac{-3}{2}$
-2, $\dfrac{-3}{2}$
2, $\dfrac{3}{2}$

Quadratic Equations

3 Likes

Answer

Given,

⇒ 2x² - x - 6 = 0

⇒ 2x² - 4x + 3x - 6 = 0

⇒ 2x(x - 2) + 3(x - 2) = 0

⇒ (2x + 3)(x - 2) = 0

⇒ 2x + 3 = 0 or x - 2 = 0 [Using Zero-product rule]

⇒ 2x = -3 or x = 2

⇒ x = $-\dfrac{3}{2}$ or x = 2

Hence, option 2 is the correct option.

Answered By

3 Likes

Mathematics

The roots of the quadratic equation 2x² - x - 6 = 0 are:
-2, $\dfrac{3}{2}$
2, $\dfrac{-3}{2}$
-2, $\dfrac{-3}{2}$
2, $\dfrac{3}{2}$

Quadratic Equations

Answer

Related Questions

Which of the following is a quadratic equation?
x² + 1 = (2 - x)² + 3
2x² + 3 = (5 + x)(2x - 3)
x³ - x² = (x - 1)³
none of these

Which of the following is not a quadratic equation?
3x - x² = x² + 5
(x + 2)² = 2(x² - 5)
$(\sqrt{2}x + 3)^{2} = 2x^{2} + 6$
(x - 1)² = 3x² + x - 2

Which of the following quadratic equations has 2 and 3 as its roots?
x² - 5x + 6 = 0
x² + 5x + 6 = 0
x² - 5x - 6 = 0
x² + 5x - 6 = 0

Which of the following is a root of the quadratic equation, 3x² + 13x + 14 = 0 ?
$-\dfrac{1}{3}$
$-\dfrac{3}{2}$
$-\dfrac{5}{3}$
$-\dfrac{7}{3}$

Mathematics

The roots of the quadratic equation 2x2 - x - 6 = 0 are:-2, 32\dfrac{3}{2}23​2, −32\dfrac{-3}{2}2−3​-2, −32\dfrac{-3}{2}2−3​2, 32\dfrac{3}{2}23​

Quadratic Equations

Answer

Related Questions

Which of the following is a quadratic equation?x2 + 1 = (2 - x)2 + 32x2 + 3 = (5 + x)(2x - 3)x3 - x2 = (x - 1)3none of these

Which of the following is not a quadratic equation?3x - x2 = x2 + 5(x + 2)2 = 2(x2 - 5)(2x+3)2=2x2+6(\sqrt{2}x + 3)^{2} = 2x^{2} + 6(2​x+3)2=2x2+6(x - 1)2 = 3x2 + x - 2

Which of the following quadratic equations has 2 and 3 as its roots?x2 - 5x + 6 = 0x2 + 5x + 6 = 0x2 - 5x - 6 = 0x2 + 5x - 6 = 0

Which of the following is a root of the quadratic equation, 3x2 + 13x + 14 = 0 ?−13-\dfrac{1}{3}−31​−32-\dfrac{3}{2}−23​−53-\dfrac{5}{3}−35​−73-\dfrac{7}{3}−37​

The roots of the quadratic equation 2x² - x - 6 = 0 are:
-2, $\dfrac{3}{2}$
2, $\dfrac{-3}{2}$
-2, $\dfrac{-3}{2}$
2, $\dfrac{3}{2}$

Which of the following is a quadratic equation?
x² + 1 = (2 - x)² + 3
2x² + 3 = (5 + x)(2x - 3)
x³ - x² = (x - 1)³
none of these

Which of the following is not a quadratic equation?
3x - x² = x² + 5
(x + 2)² = 2(x² - 5)
$(\sqrt{2}x + 3)^{2} = 2x^{2} + 6$
(x - 1)² = 3x² + x - 2

Which of the following quadratic equations has 2 and 3 as its roots?
x² - 5x + 6 = 0
x² + 5x + 6 = 0
x² - 5x - 6 = 0
x² + 5x - 6 = 0

Which of the following is a root of the quadratic equation, 3x² + 13x + 14 = 0 ?
$-\dfrac{1}{3}$
$-\dfrac{3}{2}$
$-\dfrac{5}{3}$
$-\dfrac{7}{3}$