For the equation given below, find the value of 'm' so that the equation has equal roots. Also, find the solution of the equation : (m - 3)x 2 - 4x + 1 = 0

Since, equation has equal roots, D = 0. ∴ b 2 - 4ac = 0 ⇒ (-4) 2 - 4(m - 3)(1) = 0 ⇒ 16 - 4m + 12 = 0 ⇒ 4m = 28 ⇒ m = 7. Substituting m = 7 in (m - 3)x 2 - 4x + 1 = 0 we get, ⇒ (7 - 3)x 2 - 4x + 1 = 0 ⇒ 4x 2 - 4x + 1 = 0 ⇒ 4x 2 - 2x - 2x + 1 = 0 ⇒ 2x(2x - 1) - 1(2x - 1) = 0 ⇒ (2x - 1)(2x - 1) = 0 ⇒ (2x - 1) = 0 or (2x - 1) = 0 ⇒ x = . Hence, m = 7 and x = .

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

View Answer Bookmark Now

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

View Answer Bookmark Now

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

View Answer Bookmark Now

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.

View Answer Bookmark Now

Mathematics

For the equation given below, find the value of 'm' so that the equation has equal roots. Also, find the solution of the equation :
(m - 3)x² - 4x + 1 = 0

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

For the equation given below, find the value of 'm' so that the equation has equal roots. Also, find the solution of the equation :(m - 3)x2 - 4x + 1 = 0

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.

For the equation given below, find the value of 'm' so that the equation has equal roots. Also, find the solution of the equation :
(m - 3)x² - 4x + 1 = 0

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.