Algebra

Quadratic Discriminant

Quadratic Discriminant - Determining Types of Roots

         

Which of the following equations has two distinct real roots?

(A) x2x+1=0(B) 16x2+8x+1=0(C) 25x2+310x+15=0(D) x2+5x+4=0\begin{array}{c}&(A)~x^2-x+1=0 &&(B)~16x^2+8x+1=0\\ (C)~\frac{2}{5}x^2+\frac{3}{10}x+\frac{1}{5}=0 &&(D)~x^2+5x+4=0 \end{array}

If a<3,a < 3, which of the following is true about the quadratic equation: x2+2ax+a23a+11=0?x^2+2ax+a^2-3a+11=0 ?

If the quadratic equation x2+7xk=0x^2+7x-k=0 has real roots, and the quadratic equation x22xk=0x^2-2x-k=0 has non-real complex roots, what is the range of k?k?

How many distinct real roots does the following equation have: (x2+x+4)(x2+6x+8)=0?(x^2+x+4)(x^2+6x+8)=0?

Which of the following is true about the quadratic equation: 41x220x+4=5x2+4x?41x^2-20x+4=5x^2+4x?

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