## Relation between Roots and Coefficient - Basic

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 ≠ 0. If a = 0, then the equation is linear, not quadratic, as there is no term.

Q1.  If A.M. of the roots of a quadratic equation is 8/5 and A.M. of their reciprocals is 8/7, then the equation is

•   5x2-16x+7=0
•  7x2-16x+7=0
•  7x2+16x+7=0
•   3x2-16x+7=0

5x2-16x+7=0

Q2.  The quadratic in t, such that A.M. of its roots is A and G.M. is G, is

•  t2-2At+g2=0
•  t2+2At+g2=0
•  t2-2At+g-2=0
•  t2+2At+g-2=0

t2-2At+g2=0

Q3.  In a triangle ABC, the value of angle A is given by 5cosA + 3 , then the equation whose roots are sin A and tan A will be

•   15x2-8x-16=0
•  15x2+8x-16=0
•  15x2+8x+16=0
•   None of these

15x2+8x-16=0

Q4. If x2+px+q=0 is the quadratic whose roots are a-2 and b-2 where a and b are the roots of x2-3x-1=0, then

•   p=1,q=1
•   p=-1, q=-1
•  p=1,q=-1
•  None of these

None of these

Q5.  The roots of the equation x2+ax+b=0 are p and q, then the equation whose roots are p2q and pq2 will be

•  x2+abx+b3=0
•  x2-abx+b3=0
•  x2+abx-b3=0
•  None of these

x2+abx+b3=0

Q6.  The equation whose roots are reciprocal of the roots of the equation 3x2-20x+17=0 is

•   15x2-20x+3=0
•   17x2-20x+3=0
•   15x2-20x-3=0
•  None of these

17x2-20x+3=0

Q7.  The sum of the roots of a equation is 2 and sum of their cubes is 98, then the equation is

•   x2+2x+15=0
•  2x2-2x+15=0
•  2x2+2x-15=0
•  x2-2x-15=0

x2-2x-15=0

Q8.  Sum of roots is –1 and sum of their reciprocals is 1/6 , then equation is

•  x2+x-6=0
•   x2-x+6=0
•   -2x-2+x-6=0
•   None of these

x2+x-6=0

Q9.  In the equation x2+px+q=0 , the coefficient of x was taken as 17 in place of 13 and its roots were found to be –2 and –15. The correct roots of the original equation are

•  -10,-3
•   3,10
•   -10,3
•  -3,10

-10,-3

Q10.  Two students while solving a quadratic equation in x, one copied the constant term incorrectly and got the roots 3 and 2. The other copied the constant term and coefficient of x2 correctly as – 6 and 1 respectively. The correct roots are

•   3, – 2
•   – 3, 2
•   – 6, –1
•  6, –1

6, –1

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