(ii) 8x square - 14x - 15
find the zeroes of this quadratic polynomial and verify the relationship between the zeroes and coefficients..
Answers
EXPLANATION.
Quadratic Polynomial,
⇒ F(x) = 8x² - 14x - 15.
As we know that,
Factorizes this equation into middle term split, we get.
⇒ 8x² - 14x - 15.
⇒ 8x² - 20x + 6x - 15 = 0.
⇒ 4x(2x - 5) + 3(2x - 5) = 0.
⇒ (4x + 3)(2x - 5) = 0.
⇒ x = -3/4 and x = 5/2.
As we know that,
Product of equations = (-3/4)(5/2) = -15/8.
Sum of equations = -3/4 + 5/2 = -3 + 10/4 = 7/4.
As we know that,
Sum of zeroes of quadratic equations,
⇒ α + β = -b/a.
⇒ α + β = -(-14/8) = 7/4.
Products of zeroes of quadratic equation,
⇒ αβ = c/a.
⇒ αβ = -15/8.
HENCE PROVED.
MORE INFORMATION.
Quadratic Expression.
A polynomial of degree two of the form ax² + bx + c (a ≠ 0) is called quadratic expression.
The Quadratic Equation.
ax² + bx + c (a ≠ 0) as two roots, given by.
⇒ α = -b + √b² - 4ac/2a.
⇒ β = -b - √b² - 4ac/2a.