Which of the following quadratic equations has 2 and 3 as its roots? 1. x2 - 5x + 6 = 0 2. x2 + 5x + 6 = 0 3. x2 - 5x - 6 = 0 4. x2 + 5x - 6 = 0

Since, {2, 3} is solution set. It means 2 and 3 are roots of the equation, ∴ x = 2 or x = 3 ⇒ x - 2 = 0 or x - 3 = 0 ⇒ (x - 2)(x - 3) = 0 ⇒ (x2 - 3x - 2x + 6) = 0 ⇒ x2 - 5x + 6 = 0. Hence, option 1 is the correct option.

Mathematics

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

Quadratic Equations

3 Likes

Answer

Since, {2, 3} is solution set.

It means 2 and 3 are roots of the equation,

∴ x = 2 or x = 3

⇒ x - 2 = 0 or x - 3 = 0

⇒ (x - 2)(x - 3) = 0

⇒ (x² - 3x - 2x + 6) = 0

⇒ x² - 5x + 6 = 0.

Hence, option 1 is the correct option.

Answered By

2 Likes

Mathematics

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

Quadratic Equations

Answer

Related Questions

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

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

If x = $\dfrac{-1}{2}$ is a solution of the quadratic equation 3x² + 2kx - 3 = 0, then the value of k is:
$-\dfrac{3}{4}$
$-\dfrac{5}{4}$
$-\dfrac{9}{4}$
$-\dfrac{4}{5}$

Mathematics

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

Quadratic Equations

Answer

Related Questions

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

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​

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​

If x = −12\dfrac{-1}{2}2−1​ is a solution of the quadratic equation 3x2 + 2kx - 3 = 0, then the value of k is:−34-\dfrac{3}{4}−43​−54-\dfrac{5}{4}−45​−94-\dfrac{9}{4}−49​−45-\dfrac{4}{5}−54​

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 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

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

If x = $\dfrac{-1}{2}$ is a solution of the quadratic equation 3x² + 2kx - 3 = 0, then the value of k is:
$-\dfrac{3}{4}$
$-\dfrac{5}{4}$
$-\dfrac{9}{4}$
$-\dfrac{4}{5}$