Question 40

Which of the following equations has real and distinct roots?

Solution

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

(A) : $$3x^{2} - 6x + 2 = 0$$

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

(B) : $$3x^{2} - 6x + 3 = 0$$

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

(C) : $$x^{2} - 8x + 16 = 0$$

=> D = $$(-8)^2 - 4(1)(16) = 64 - 64 = 0$$

(D) : $$4x^{2} - 8x + 4 = 0$$

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

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

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