## Nature of roots - Advance

**Dear Readers,**

In algebra, a quadratic equation is any equation that can be rearranged in standard form as where x represents an unknown, and a, b, and c represent known numbers, where a is not equal to 0. If a = 0, then the equation is linear, not quadratic, as there is no term.

**Q1. ** If f(x) is a continuous function and attains only rational values and f(0)=3 , then roots of equation f(1)x^{2}+f(3)x+f(5)=0 are

Imaginary

**Q2. ** The roots of ax^{2}+bx+c=0 , where a is not equal to 0 and coefficients are real, are non-real complex and a+c**
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4a+c=2b

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**Q3. ** If a, b, c, d are four consecutive terms of an increasing AP then the roots of the equation (x-a)(x-c)+2(x-b)(x-d)=0 are

Real and distinct

**Q4. ** If a, b, c are three distinct positive real numbers then the number of real roots of ax^{2}+2b|x|-c=0 is

2

**Q5. ** The number of integral values of a for which x^{2}-(a-1)x+3=0 has both roots positive and x^{2}+3x+6=0 has both roots negative is

Infinite

**Q6. ** If f(x)= (x^{2}-1)/(x^{2}+1) for every real number x then the minimum value of f

Is equal to -1

**Q7. ** If a, b, c are in H.P. then the expression a(b-c)x^{2}+b(c-a)x+c(a-b)

Is a perfect square

**Q8. ** If a, b, c are in G.P., where a, c are positive, then the equation ax^{2}+bx+c=0 has

Imaginary roots

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