Find the values of m for which equation 3x 2 + mx + 2 = 0 has equal roots. Also, find the roots of the given equation.

When equation has equal roots, D = 0. ∴ b 2 - 4ac = 0 Comparing 3x 2 + mx + 2 = 0 with ax 2 + bx + c = 0 we get, a = 3, b = m and c = 2. ⇒ m 2 - 4(3)(2) = 0 ⇒ m 2 - 24 = 0 ⇒ m 2 = 24 ⇒ m = Considering, m = ⇒ 3x 2 + mx + 2 = 0 3x 2 + x + 2 = 0 3x 2 + = 0 = 0 = 0 x = . Rationalising, . Considering, m = - ⇒ 3x 2 + mx + 2 = 0 ⇒ 3x 2 - x + 2 = 0 ⇒ = 0 ⇒ = 0 ⇒ x = . Rationalising, . Hence, m = and roots = .

Solve :
(a + b)²x² - (a + b)x - 6 = 0; a + b ≠ 0.

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Without solving the following quadratic equation, find the value of 'm' for which the given equation has real and equal roots.
x² + 2(m - 1)x + (m + 5) = 0

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Find the value of k for which equation 4x² + 8x - k = 0 has real roots.

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If -2 is a root of the equation 3x² + 7x + p = 1, find the value of p. Now find the value of k so that the roots of the equation x² + k(4x + k - 1) + p = 0 are equal.

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Mathematics

Find the values of m for which equation 3x² + mx + 2 = 0 has equal roots. Also, find the roots of the given equation.

Quadratic Equations

Related Questions

Solve :
(a + b)²x² - (a + b)x - 6 = 0; a + b ≠ 0.

Without solving the following quadratic equation, find the value of 'm' for which the given equation has real and equal roots.
x² + 2(m - 1)x + (m + 5) = 0

Find the value of k for which equation 4x² + 8x - k = 0 has real roots.

If -2 is a root of the equation 3x² + 7x + p = 1, find the value of p. Now find the value of k so that the roots of the equation x² + k(4x + k - 1) + p = 0 are equal.

Mathematics

Find the values of m for which equation 3x2 + mx + 2 = 0 has equal roots. Also, find the roots of the given equation.

Quadratic Equations

Related Questions

Solve :(a + b)2x2 - (a + b)x - 6 = 0; a + b ≠ 0.

Without solving the following quadratic equation, find the value of 'm' for which the given equation has real and equal roots.x2 + 2(m - 1)x + (m + 5) = 0

Find the value of k for which equation 4x2 + 8x - k = 0 has real roots.

If -2 is a root of the equation 3x2 + 7x + p = 1, find the value of p. Now find the value of k so that the roots of the equation x2 + k(4x + k - 1) + p = 0 are equal.

Find the values of m for which equation 3x² + mx + 2 = 0 has equal roots. Also, find the roots of the given equation.

Solve :
(a + b)²x² - (a + b)x - 6 = 0; a + b ≠ 0.

Without solving the following quadratic equation, find the value of 'm' for which the given equation has real and equal roots.
x² + 2(m - 1)x + (m + 5) = 0

Find the value of k for which equation 4x² + 8x - k = 0 has real roots.

If -2 is a root of the equation 3x² + 7x + p = 1, find the value of p. Now find the value of k so that the roots of the equation x² + k(4x + k - 1) + p = 0 are equal.