Question 89

Which of the following equations has equal roots?

Solution

A quadratic equation : $$ax^2 + bx + c = 0$$ has equal roots iff Discriminant, $$D = b^2 - 4ac = 0$$

(A) : $$3x{2}-6x+2=0$$

=> D = $$(-6)^2 - 4(3)(2) = 36 - 24 = 12 \neq 0$$

(B) : $$3x^{2}-6x+3=0$$

=> D = $$(-6)^2 - 4(3)(3) = 36 - 36 = 0$$

(C) : $$x^{2}-8x+8=0$$

=> D = $$(-8)^2 - 4(1)(8) = 64 - 32 = 32 \neq 0$$

(D) : $$4x^{2}-8x+2=0$$

=> D = $$(-8)^2 - 4(4)(2) = 64 - 32 = 32 \neq 0$$

Thus, the equation : $$3x^{2}-6x+3=0$$ has equal roots.


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