Question

Find the zeroes and verify the relationship b/w zeroesand coefficients:-
(i)x^2+x-12
(ii)3x^2-3root3x+2
​

Answer 1

Answer:

(i) -4 and +3

(ii) 1/√3 and 2/√3

Step-by-step explanation:

(i) x^2 +x -12

Solving for zeroes , we get,

=> x^2 + 4x -3x -12 = 0

=> x(x+4)-3(x+4)=0

=>(x+4)(x-3)=0

Therefore, we have,

=> x = -4

And

=> x = +3

Now, we have,

Sum of roots = -4+3 = -1 = -1/1 = -b/a

Product of roots = -4(3) = -12 = -12/1 = c/a

Thus, Verified.

(ii) 3x^2 -3√3x +2

Solving for roots, we get,

=> 3x^2 -√3x -2√3x +2 = 0

=> √3x(√3x-1)-2(√3x-1)=0

=> (√3x-1)(√3x-2)=0

Therefore, we have,

=> x = 1/√3

And

=> x = 2/√3

Now, we have,

Sum of roots = 3/√3 = √3 = -(-3√3/3) = -b/a

Product of roots = 1/√3 × 2/√3= 2/3 = c/a

Thus, verified.