Question

6x²-3-7x find the zeros of tha quadratic polynomial​ and find the relationship between zeros​

Answer 1

Given

We have given an equation : 6x²-7x-3

To Find

We have to find the zeroes and verify the relationship between zeroes and it's coefficients

$\sf\huge {\underline{\underline{{Solution}}}}$

=> 6x²-7x-3

=> 6x²-9x+2x-3

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

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

Makes equal to zero,we get

=> (3x+1)(2x-3)=0

x= -1/3 & x= 3/2

Let the two zeroes be λ and β

From above Equation

a= 6,b= -7 and c = -3

Sum of zeroes= -b/a

λ + β = -b/a

-1/3+3/2

-2+9/6= 7/6

λ+ β= 7/6

-b/a= -(-7)6= 7/6

Product of zeroes = c/a

λ * β= -1/3*3/2= -3/6= -1/2

c/a= -3/6= -1/2

Hence,the relationship between the zeroes and it's coefficients verified.

Answer 2

Step-by-step explanation:

Given

We have given an equation : 6x²-7x-3

To Find

We have to find the zeroes and verify the relationship between zeroes and it's coefficients

\sf\huge {\underline{\underline{{Solution}}}}

Solution

=> 6x²-7x-3

=> 6x²-9x+2x-3

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

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

Makes equal to zero,we get

=> (3x+1)(2x-3)=0

x= -1/3 & x= 3/2

Let the two zeroes be λ and β

From above Equation

a= 6,b= -7 and c = -3

Sum of zeroes= -b/a

λ + β = -b/a

-1/3+3/2

-2+9/6= 7/6

λ+ β= 7/6

-b/a= -(-7)6= 7/6

Product of zeroes = c/a

λ * β= -1/3*3/2= -3/6= -1/2

c/a= -3/6= -1/2

Hence,the relationship between the zeroes and it's coefficients verified.