Question

7. Find the zeroes of the quadratic polynomial p(x)=6x2 -3-7x.
8. Find a quadratic polynomial whose sum and product of its zeroes are 1/4 and -1 respectively.
I
9. Find the zeroes of the polynomial x2 – 3 and verify the relationship between the zeroes and
efficients​

Answer 1

Answer: 6x²-7x-3 for question 7

Step-by-step explanation: =6x²-7x-3

=6x²+2x-9x-3

=2x(3x+1)-3(3x+1)

=(2x-3)(3x+1)

⇒2x-3=0                                    or                            ⇒3x+1=0

⇒x=3/2                                       or                           ⇒ x= - 1/3

α=3/2 ,β= - 1/3

⇒α+β= -b/a

⇒3/2+(-1/3)= - (-3)/6

⇒3/2-1/3=1/2

⇒7/6 =1/2

⇒αβ=c/a

⇒ 3/2(-1/3)= -7/6

⇒-1/2= -7/6

⇒1/2=7/6      

Answer 2

Answer:

7. p(x)=6x^2-7x-3

=6x^2+9x-2x-3

=3x(2x+3)-1(2x+3)

=(2x+3)(3x-1)

now,

applying zero product rule,

2x+3=0 & 3x-1=0

x=-3/2 x=1/3

therefore, the zeroes are -3/2 &1/3

8.Given,

sum of zeroes=1/4

-b/a =1/4 -----------(i)

product of zeroes=-1

c/a=-1 ------------(ii)

from (i) and (ii) ,

a=4

b=-1

c=-4

therefore,

p(x)=ax^2+bx+c

=4x^2+(-1)x+(-4)

=4x^2-x-4

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