Find the zeroes of the quadratic polynomial p(x) = 4x2 - 2 - 10x, and verify the relationship between the
zeroes and the coefficients.
Solve 2x + 3y = 11 and 2x - 4y = -24 and hence find the value of 'p' for which y = px - 4.
Answers
Given : quadratic polynomial p(x) = 4x² - 2 - 10x
To Find : the zeroes
verify the relationship between the zeroes and the coefficients.
Solution:
p(x) = 4x² - 2 - 10x
4x² - 10x - 2 = 0
Zeroes = { -(-10) ± √(-10)² - 4(4)(-2) } /( 2 * 4)
= (10 ± √132)/8
= ( 5 ± √33)/4
Zeroes are ( 5 + √33)/4 , ( 5 - √33)/4
Sum of Zeroes = ( 5 + √33)/4 + ( 5 - √33)/4 = 10/4 = 5/2
Product of Zeroes = {( 5 + √33)/4 } *{ ( 5 - √33)/4 } = (25 - 33)/4 = -8/16 = -1/2
4x² - 10x - 2
Sum of zeroes = - (-10)/4 = 5/2
Product of zeroes = -2/4 = - 1/2
Verified
2x + 3y = 11
2x - 4y = -24
=> 7y = 35
=> y = 5
=> x = -2
y = px - 4
=> 5 = p(-2) - 4
=> p = -9/2
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