Question

Q 1. The quadratic polynomial whose sum of zeroes is 3 and product of zeroes is –2 is
: (a) x 2 + 3x – 2(b) x 2 – 2x + 3(c) x 2 – 3x + 2(d) x 2 – 3x – 2
Q 2. The number of zeroes that polynomial f(x) = (x – 2) 2 + 4 can have is:
(a) 1(b) 2(c) 0(d) 3
Q 3. Graph of a quadratic polynomial is a
(a) straight line(b) circle(c) parabola(d) ellipse
Q 4. A polynomial of degree n has
(a) only 1 zero(b) exactly n zeroes(c) atmost n zeroes(d) more than n zeroes
Q5. If p(x) = ax 2 + bx + c, then -b/a is equal to
(a) 0(b) 1(c) sum of zeroes(d) product of zeroes
Q6. If p(x) = ax 2 + bx + c, then c/a is equal to
(a) 0(b) 1(c) product of zeroes(d) sum of zeroes
Q7. A quadratic polynomial whose one zero is 6 and sum of the zeroes is 0, is
(a) x 2 �� 6x + 2(b) x 2 – 36(c) x 2 – 6(d) x 2 – 3
Q8. If p(x) = ax + b, then zero of p(x)
(a) a (b) b (c) -b/a (d) -a/b
Q9. If p(x) is a polynomial of at least degree one and p(k) = 0, then k is known as
(a) value of p(x) (b) zero of p(x) (c) constant term of p(x) (c) none of these
Q 10.Zeroes of a polynomial can be determined graphically. No. of zeroes of a polynomial is equal to no. of points where the graph of polynomial
(a) intersects y-axis (b) intersects x-axis (c) intersects y-axis or intersects x-axis (d) none of these

Answer 1

Given :  Questions regarding Quadratic Equations

To find : Solution

Solution:

Q 1. The quadratic polynomial whose sum of zeroes is 3 and product of zeroes is –2 is

x² - (Sum of zeroes)x  + Product of Zeroes =  0

x² - 3x  - 2  = 0  

f(x) = (x – 2)² + 4

(x – 2)²  ≥ 0

=> f(x) ≥ 4

Hence no real Zeroes of f(x)

Graph of a quadratic polynomial is a parabola

A polynomial of degree n has  atmost n zeroes

Q5. If p(x) = ax 2 + bx + c, then -b/a is equal to   sum of zeroes

Q6. If p(x) = ax 2 + bx + c, then c/a is equal to product of zeroes

A quadratic polynomial whose one zero is 6 and sum of the zeroes is 0

x² - 36

Q8. If p(x) = ax + b, then zero of p(x)  = -b/a

Q9. If p(x) is a polynomial of at least degree one and p(k) = 0, then k is known as  zero of p(x)

Zeroes of a polynomial can be determined graphically. No. of zeroes of a polynomial is equal to no. of points where the graph of polynomial  intersects x-axis  if we are talking about f(x)

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