Find the values of m for which the equation `x^2 -2 (5 + 2m) x+ 3 (7+ 10m) =0` has equal roots.

Find the value of k such that the equation (k - 12)x^2 - 2(k – 12)x + 2 = 0 may have equal roots.

Find the value of m for which 5^m div 5^-3 = 5^5

For what value of m will the equation x^2 -(3m - 1) x + 2m^2 + 2m - 11 =0 have equal roots? Find the roots.

The following equations have equal roots find k in each equation. x^2 - 2(5 + 2k) x + 3(7 + 10k) = 0 .

Find the value of m for which the lines 4x -3y - 1 = 0, 3x - 4y + 1 = 0 and mx - 7y + 3 = 0 are concurrent.

If the equation (a^2+b^2)x^2-2(ac+bd)x+(c^2+d^2)=0 has equal roots, then

For what value of a, the equation 3x^2 + 2 (a^2 + 1) x + (a^2 - 3a + 2) = 0 possesses roots of opposite sign?

Find the value of a and b for which x=2,3 are the roots of the equation 3x^2+2ax+2b=0

If -3 is a root of the equation x^2+ px + 6 = 0 and the equation x^2 +px +q = 0 has equal roots, find p,q .

If 2 is a root of the equation x^2+px-8 = 0 and the equation x^2 + px + q = 0 has equal roots, find p, q .