Question

9 Find all zeros of the polynomial 3x + 10x2 - 9x – 4 if one of its zeros
is 1.
[CBSE 2019]​

Answer 1

Answer:

3x^3+10x^2--9x--4

1is theroot

What are other roots

f(x) =x3+10x^2--9x--4

f(-+-1) = 3(1)^3+10(--+1)^2--9(--+1) --4

=--3+10—9--4=0

f(1)=0

(x--1) is a factor of f(x)

. By division

3x^3 +10x^2--9x--4. Divide by x--1. ( 3x^2)

3x^3--3x^2. Subtracting

13x^2 -9× Divide by x-1.( 13x)

13^x2– 13x. Subtracting

4x -4. Dividing by x-1. (4)

4x-4 subtracting

0. Reminder

3x^2+13x+-4

Factorisation of 3x^2+13x +4.

(3×4 =12. 12×1=12. 12+1 =13)

3x^2 +12x+1x+4

3x(x+4) +1(x+4)

(3x+1) (x+1)

FACTORS of given polynomial are( x+1)(3x+4) (x+1)

Answer 2

To find:All the zeroes of the polynomial 3x+10x²-9x-4.

Solution:-

$\bf {3x+10x²-9x-4}$

$\leadsto \rm {10x²-6x-4=0}$

$\leadsto \rm {10x²-(10-4)x-4=0}$

$\leadsto \rm {10x²-10x+4x-4=0}$

$\leadsto \rm {10x(x-1)+4(x-1)=0}$

$\leadsto \rm {(10x+4)(x-1)=0}$

Either,

$\rm {10x+4=0}$

$\rm {x=\frac{-4}{10}}$

$\rm {x=\frac{\cancel{-4}}{\cancel{10}}}$

$\rm {x=\frac{-2}{5}}$

Or,

$\rm {x-1=0}$

$\rm {x=1}$

Hence ,the zeroes are 1 and -2/5