Question: Which of the following polynomials has the sum of zeroes -3/2 and the product of zeroes - 1?

Posted by: Arun S. on 08.08.2017

2×2+3×(-2) sum of root =-3/2 product of the roots = -1

Sum of the zeros is (-b/a) which is -3/2

product of the zeros is c/a which is -2/2

2x^x+3x—2

Equation of a polynomial whose zeroes are p and q is following --

x2 - (p+q)x + pq = 0

Since we have given that sum of zeroes (p+q) = -3/2

product of zeroes (pq) = -1

x2 - (-3/2)x + (-1) = 0

x2 + (3/2)x + (-1) = 0

2x2 + 3x - 2 = 0

Hence option (2) is correct.

second option as sum of roots is (-b/a) and product of roots is (c/a)

Second option satifies the given condition

Answer :- option(2) , quadratic equation form :- Ax*2+Bx+C=0 Sum of zeroes = -(B/A) Product of zeroes = (C/A) In option(2) A=2 , B= 3 , C=-2 Sum of zeroes = -(3/2) Product of zeroes = (-2)/2 = -1

Standard equation for quadratic polynomial : ax2+bx+c =0, can be taken as x2+b/ax+c/a=0 (divided both sides by a). here, sum of zeros = -3/2=-b/a ,which gives b/a=3/2 product of zeros = 1= c/a putting the values of b/a and c/a in general equation, we get; x2+3/2x+1=0 , solving further..we get 2x2+3x+1=0.

2nd option has the sum of zeroes -3/2 and the product of zeroes - 1

2.

sum of zeroes=-b/a=-3/2

product of zeroes=c/a=-2/2=1

2.x.x+3.x—2=0
2x2+3x-2=ax2+bx+c Sum of roots= -b/a =-3/2 Product of roots = c/a= -2/2=-1 So answer is option 2
Standard equation for quadratic polynomial : ax2+bx+c =0, can be taken as x2+b/ax+c/a=0 (divided both sides by a). here, sum of zeros = -3/2=-b/a ,which gives b/a=3/2 product of zeros = 1= c/a putting the values of b/a and c/a in general equation, we get; x2+3/2x+1=0 , solving further..we get 2x2+3x+1=0.
2x2+3x-2 sum of root = -3/2 product of roots= -1

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