Class 10 Maths: Relationship Between Zeroes and Coefficients of a Polynomial

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Class 10 Maths Exercise 2.2

1. Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients.

$$ (i) x^2-2x-8 \qquad (ii) 4s^2-4s+1 \qquad (iii) 6x^-3-7x $$
$$ (iv) 4u^2+8u \qquad (v) t^2-15 \qquad (vi) 3x^2-x-4$$

... Answers:
$$ (i) -2, 4 \qquad (ii) 1/2, 1/2 \qquad (iii) - 1/3 , 3/2 $$
$$ (iv) -2, 0 \qquad (v)-√15, √15 \qquad (vi) -1, 4/3 $$

2. Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively.

$$ (i) {1\over4}, 1\qquad (ii) {\sqrt2}, {1\over3} \qquad (iii) 0, {\sqrt5} $$
$$(iv) 1, 1 \qquad (v) -{1\over4} ,{1\over4}\qquad (vi) 4,1 $$

... Answers:
$$ (i) 4x^2-x-4 \qquad (ii) 3x^2-3√2x+1 \qquad (iii) x^2+√5 $$
$$ (iv) x^2-x+1 \qquad (v)4x^2+x+1 \qquad (vi) x^2-4x+1 $$