Question

2x²-7x+3=0 and verify the relationship

Answer 1

Question should be:

• Find the zeros of Quadratic equation 2x²-7x+3 = 0 and verify the relationship between zeros and their coefficient.

ANSWER:

• Zeros are 3 and 1/2

GIVEN:

• 2x²-7x+3 = 0

TO FIND:

• Zeros and verify the relationship between zeros and coefficients.

SOLUTION:

=> 2x²-7x+3 = 0

=> 2x²-6x-x+3 = 0

=> (2x²-6x)+(-x+3) = 0

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

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

Either (x-3) = 0

=> x = 3

Either (2x-1) = 0

=> 2x = 1

=> x = 1/2

Formula:

=> Sum of zeros (α+β) = -(Coefficient of x)/Coefficient of x²

=> Product of zeros (αβ) = Constant term/ Coefficient of x²

Sum of zeros :

$= 3 + \dfrac{1}{2} \\ \\ \implies \dfrac{ - (-7)}{2} = \dfrac{ - (coefficient \: ofx)}{coefficient \: of \: x {}^{2} } \:$

Product of zeros

$\: = 3 \times \dfrac{1}{2} \\ \\ \implies \dfrac{3}{2} = \dfrac{constant \: term}{coefficient \: of \: x {}^{2} }$