Find the value(s) of p for which the quadratic equation (2p + 1)x 2 - (7p + 2)x + (7p - 3) = 0 has equal roots. Also find these roots.

The given equation is (2p + 1)x 2 - (7P + 2)x + (7p - 3) = 0. Comparing with ax 2 + bx + c = we obtain, a = 2p + 1 , b = -(7p + 2) , c = 7p - 3 For equal roots, discriminant = 0 When p = the equation becomes so the roots are : When p = 4 the equation becomes so the roots are : (Ans.) 4, ; when p = , roots are 7, 7 and when p = 4, roots are

Find the value(s) of m for which each of the following quadratic equation has real and equal roots :
(i) (3m + 1)x² + 2(m + 1)x + m = 0
(ii) x² + 2(m - 1)x + (m + 5) = 0

View Answer Bookmark Now

Find the values of k for which each of the following quadratic equation equal roots :
(i) 9x² + kx + 1 = 0
(ii) x² - 2kx + 7k - 12 = 0 Also, find the roots for those values of k in each case.

View Answer Bookmark Now

Find the value(s) of p for which the quadratic equation 2x² + 3x + p = 0 has real roots.

View Answer Bookmark Now

Find the least positive value of k for which the equation x² + kx + 4 = 0 has real roots.

View Answer Bookmark Now

Mathematics

Find the value(s) of p for which the quadratic equation (2p + 1)x² - (7p + 2)x + (7p - 3) = 0 has equal roots. Also find these roots.

Quadratic Equations

Related Questions

Find the value(s) of m for which each of the following quadratic equation has real and equal roots :
(i) (3m + 1)x² + 2(m + 1)x + m = 0
(ii) x² + 2(m - 1)x + (m + 5) = 0

Find the values of k for which each of the following quadratic equation equal roots :
(i) 9x² + kx + 1 = 0
(ii) x² - 2kx + 7k - 12 = 0 Also, find the roots for those values of k in each case.

Find the value(s) of p for which the quadratic equation 2x² + 3x + p = 0 has real roots.

Find the least positive value of k for which the equation x² + kx + 4 = 0 has real roots.

Mathematics

Find the value(s) of p for which the quadratic equation (2p + 1)x2 - (7p + 2)x + (7p - 3) = 0 has equal roots. Also find these roots.

Quadratic Equations

Related Questions

Find the value(s) of m for which each of the following quadratic equation has real and equal roots :(i) (3m + 1)x2 + 2(m + 1)x + m = 0(ii) x2 + 2(m - 1)x + (m + 5) = 0

Find the values of k for which each of the following quadratic equation equal roots :(i) 9x2 + kx + 1 = 0(ii) x2 - 2kx + 7k - 12 = 0 Also, find the roots for those values of k in each case.

Find the value(s) of p for which the quadratic equation 2x2 + 3x + p = 0 has real roots.

Find the least positive value of k for which the equation x2 + kx + 4 = 0 has real roots.

Find the value(s) of p for which the quadratic equation (2p + 1)x² - (7p + 2)x + (7p - 3) = 0 has equal roots. Also find these roots.

Find the value(s) of m for which each of the following quadratic equation has real and equal roots :
(i) (3m + 1)x² + 2(m + 1)x + m = 0
(ii) x² + 2(m - 1)x + (m + 5) = 0

Find the values of k for which each of the following quadratic equation equal roots :
(i) 9x² + kx + 1 = 0
(ii) x² - 2kx + 7k - 12 = 0 Also, find the roots for those values of k in each case.

Find the value(s) of p for which the quadratic equation 2x² + 3x + p = 0 has real roots.

Find the least positive value of k for which the equation x² + kx + 4 = 0 has real roots.