Question

Home Work :- Find zeroes
verify the relationship between
Zeroes and the coefficients.

$2 x2 - 3x + 1$
​

Answer 1

QUESTION:

• Find zeroes and verify the relationship between Zeroes and the coefficients. P(x) = 2x²-3x+1

ANSWER:

• Zeros are 1 and 1/2

GIVEN:

• P(x) = 2x²-3x+1

TO VERIFY:

• Relationship between Zeroes and the coefficients.

SOLUTION:

P(x) = 2x²-3x+1

Finding zeros :

=> 2x²-3x+1 = 0

=> 2x² -2x-x +1 = 0

=> (2x²-2x) +(-x+1) = 0

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

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

Either,. (x-1) = 0

=> x = 1

Either ,. (2x-1) = 0

=> 2x = 1

=> x = 1/2

Now verifying:

Sum of zeros:

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

Product of zeros:

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

Verified.