find the zeros of the following quaratic polynomial and verify the relationship between the zeros and the coefficient: 6x²-3-7x About the author Margaret
Given We have given a quadratic equation 6x²-7x-3 To Find We have to find zeros of given Equation and hence verify it’s relationship between the zeroes. [tex]\sf\huge\bold{\underline{\underline{{Solution}}}}[/tex] Firstly we have to find the zeroes ➞6x²-7x-3 ➞6x²-9x+2x-3 ➞3x(2x-3)+1(2x-3) ➞(3x+1)(2x-3)=0 ➞3x+1=0 x= -1/3 ➞2x-3=0 x= 3/2 Now, verifying the relationship 6x²-7x-3 a= 6 ,b = -7 & c= -3 Let λ = -1/3 & β = 3/2 Sum of its zeroes = -b/a λ+β= -b/a ➞ -1/3 +3/2 = -(-7/6) ➞-2+9/6= 7/6 ➞7/6 = 7/6 Product of its zeroes = c/a λβ= c/a ➞ -1/3×3/2= -3/6 ➞-3/6 = -3/6 ➞-1/2 = -1/2 Hence,the relationship between the zeroes and the coefficient is verified. Reply
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Given
We have given a quadratic equation 6x²-7x-3
To Find
We have to find zeros of given Equation and hence verify it’s relationship between the zeroes.
[tex]\sf\huge\bold{\underline{\underline{{Solution}}}}[/tex]
Firstly we have to find the zeroes
➞6x²-7x-3
➞6x²-9x+2x-3
➞3x(2x-3)+1(2x-3)
➞(3x+1)(2x-3)=0
➞3x+1=0
x= -1/3
➞2x-3=0
x= 3/2
Now, verifying the relationship
6x²-7x-3
a= 6 ,b = -7 & c= -3
Let λ = -1/3 & β = 3/2
Sum of its zeroes = -b/a
λ+β= -b/a
➞ -1/3 +3/2 = -(-7/6)
➞-2+9/6= 7/6
➞7/6 = 7/6
Product of its zeroes = c/a
λβ= c/a
➞ -1/3×3/2= -3/6
➞-3/6 = -3/6
➞-1/2 = -1/2
Hence,the relationship between the zeroes and the coefficient is verified.