Question

Find the zeroes of the following quadratic polynomials and verify the relationships between the zeroes and the coefficients of the polynomials:-
(a) p(x) = 8x2 – 19x – 15
​​(b) q(x) = 4 3 x 2 + 5x – 2 3 ​
(c) f (x) = 5x - 4 3 + 2

Answer 1

(a) p(x) = 8x2 – 19x – 15

Relationship between zeroes and coefficients

Sum of zeroes=-(coefficient of x)/coefficient of x^2=-(-19)/8=19/8

Product of zeroes=constant term/coefficient of x^2=-15/8

(b) q(x) = 4 3 x 2 + 5x – 2 3

Relationship between zeroes and coefficients

Sum of zeroes=-(coefficient of x)/coefficient of x^2=-5/43

Product of zeroes=constant term/coefficient of x^2=-23/43

(c) f (x) = 5x2 - 43x + 2

Relationship between zeroes and coefficients

Sum of zeroes=-(coefficient of x)/coefficient of x^2=-(-43)/5=43/5

Product of zeroes =constant term/coefficient of x^2=2/5

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