Consider the quadratic equation with real coefficients .

MATHEMATICS · Multi-part · A Level · Mathematics · Algebra and Functions · Algebra and Functions

Problem

Consider the quadratic equation ax2+bx+c=0ax^{2}+bx+c=0 with real coefficients a≠0a\neq 0. (i) Define its discriminant and state how the value of the discriminant determines the nature of its roots. (ii) Hence prove that the equation possesses equal real roots if and only if b2=4acb^{2}=4ac. (iii) Using the above result, determine all values of kk for which the equation 3x2+(2k−5)x+(k2−4)=03x^{2}+(2k-5)x+(k^{2}-4)=0 has equal roots.

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