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31). If $$\Large \alpha , \beta$$ are the roots of equation $$\Large ax^{2}+bx+c=0$$, then $$\Large \frac{ \alpha }{ \alpha \beta +b}+\frac{ \beta }{ \alpha x+b}$$ is equal to
 A). 2/a B). 2/b C). 2/c D). -2/a
32). If the roots of the equation $$\Large \frac{ \alpha }{x- \alpha }+\frac{ \beta }{x- \beta }=1$$ be equal in magnitude but opposite in sign, then $$\Large \alpha + \beta$$ is equal to:
 A). 0 B). 1 C). 2 D). none of these
33). If the roots of the equation $$\Large px^{2}+2qx+r=0$$ and $$\Large qx^{2}-2\sqrt{pr}x+q=0$$ be real, then:
 A). $$\Large p=q$$ B). $$\Large q^{2}=pr$$ C). $$\Large p^{2}=qr$$ D). $$\Large r^{2}=pq$$
34). If one root of the quadratic equation $$\Large ax^{2}+bx+c=0$$ is equal to nth power of the other root, then the value of $$\Large \left(ac^{n}\right)^{\frac{1}{n+1}} + \left(a^{n}c\right)^{\frac{1}{n+1}}$$ is equal to
 A). b B). -b C). $$\Large b^{1/n+1}$$ D). $$\Large -b^{1/n+1}$$
35). The quadratic in t, such that AM of its roots is A and GM is G is:
 A). $$\Large t^{2}-2At+G^{2}=0$$ B). $$\Large t^{2}-2At-G^{2}=0$$ C). $$\Large t^{2}+2At+G^{2}=0$$ D). none of these.

36). If $$\Large n^{2}px+1$$ is a factor of expression $$\Large ax^{3}+bx+c$$ then:
 A). $$\Large a^{2}+c^{2}=-ab$$ B). $$\Large a^{2}-c^{2}=-ab$$ C). $$\Large a^{2}-c^{2}=ab$$ D). none of these
37). If $$\Large \sqrt{3x^{2}-7x-30} + \sqrt{2x^{2}-7x-5} = x+5$$, then x is equal to:
 A). 2 B). 3 C). 6 D). 5
38). The value $$\Large 2+\frac{1}{2+\frac{1}{2+........\infty}}$$
 A). $$\Large 1-\sqrt{2}$$ B). $$\Large 1+\sqrt{2}$$ C). $$\Large 1\pm \sqrt{2}$$ D). none of these
39). If the roots of the equation $$\Large qx^{2}+px+q=0$$ are complex, where p, q are real then the roots of the equation $$\Large x^{2}-4qx+p^{2}=0$$ are:
 A). real and unequal B). real and equal C). imaginary D). none of these
40). The number or real solution of the equation $$\Large x^{2}-3|x|+2=0$$ is:
 A). 2 B). 4 C). 1 D). 3
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