Quadratic Equation
1. Find the value of k for which the equation has real and equal roots (k+4)x² + (k+1)x + 1 = 0
2. If -5 is a root of the quadratic equation 2x²+px-15=0 and the quadratic equation p(x²+x) + k = 0 has equal roots, find the value of k?
3. If the roots of the equation (b-c)x² + (c-a)x +(a-b) = 0 are real and equal then prove that 2b= a+c
4. If equation (1+m²)x² + 2mcx + (c²-a²) = 0 has equal roots, prove that c² = a²(1+m²)
5. Find the values of k for which the quadratic equation x²-kx+9 = 0 has real and distinct roots.