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

For real roots, Discriminant ≥ 0 or , b 2 - 4ac ≥ 0 The above equation is 2x 2 + 3x + p = 0 Comparing with ax 2 + bx + c = we obtain, a = 2 , b = 3 , c = p Putting values in b 2 - 4ac ≥ 0 we get, Hence the value of p is ≤ .

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.

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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.

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

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Find the values of p for which the equation 3x² - px + 5 = 0 has real roots.

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Mathematics

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

Quadratic Equations

Related Questions

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 (2p + 1)x² - (7p + 2)x + (7p - 3) = 0 has equal roots. Also find these roots.

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

Find the values of p for which the equation 3x² - px + 5 = 0 has real roots.

Mathematics

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

Quadratic Equations

Related Questions

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 (2p + 1)x2 - (7p + 2)x + (7p - 3) = 0 has equal roots. Also find these roots.

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

Find the values of p for which the equation 3x2 - px + 5 = 0 has real roots.

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

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 (2p + 1)x² - (7p + 2)x + (7p - 3) = 0 has equal roots. Also find these roots.

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

Find the values of p for which the equation 3x² - px + 5 = 0 has real roots.