Question

1. Find the zeroes of
polynomial 4t? + 8t.
2. Write sum and product
of zeroes of polynomial
3x? - X - 4.
3. Find the zeroes of the
polynomial X? - 3.
4. Find the zeroes of the
quadratic polynomial x? +
5x + 6.
5. Write the polynomial
whose zeroes are -5 and 4
is :
(A) x2 - X + 20
(B) x² + X-20
(C) x2 - X-20
(D) x² + x+ 20
6. The zeroes of the
quadratic polynomial x? +
5x + 6 are:
(A) One positive and one
negative
(B) both equal
(C) both negative
(D) both positive​

Answer 1

Now,

3x

2

−x−4

=3x

2

−4x+3x−4

=x(3x−4)+1(3x−4)

=(3x−4)(x+1).

So the zeroes of the polynomial are x=

3

4

and x=−1.

f(v)=v2+4

√

3

v-15

(xi) p(y)=y2+

3

√

5

2

y-5

(xii) q(y)=7y2-

11

3

y-

2

3

ANSWER:

(i) We have,

f(x) = x2 − 2x − 8

f(x) = x2 + 2x − 4x − 8

f(x) = x (x + 2) − 4(x + 2)

f(x) = (x + 2) (x − 4)

The zeros of f(x) are given by

f(x) = 0

x2 − 2x − 8 = 0

(x + 2) (x − 4) = 0

x + 2 = 0

x = −2

Or

x − 4 = 0

x = 4

Thus, the zeros of f(x) = x2 − 2x − 8 are α = −2 and β = 4

We have,

h(t) = t2 − 15h(t) = (t)2 − (15−−√)2h(t) = (t + 15−−√) (t − 15−−√)

The zeros of are given by

h(t) = 0(t − 15−−√) (t + 15−−√) = 0(t − 15−−√) = 0t = 15−−√or (t + 15−−√) = 0t = −15−−√

Hence, the zeros of h(t) are α = 15−−√ and β = − 15−−√.