Question

If a quadratic polynomial $y=ax^{2}+bx +c$ intersects x axis at α and β, then
(a) α + β = -b/a
(b) α + β = a/b
(c) α × β = a/c
(d) α/β = 1

Answer 1

Answer:

(a) -b / a

Hello.  I hope this helps!

Step-by-step explanation:

The curve intersects the x-axis at α and β

=> α and β are roots, the values of x that make y = 0

=> ax² + bx + c = a ( x - α ) ( x - β )

=> ax² + bx + c = a ( x² - ( α + β ) x + αβ )

=> ax² + bx + c = ax² - a ( α + β ) x + aαβ

=> b = -a ( α + β )

=> α + β = -b / a

Answer 2

Answer:

Substitute the value of x in the equation y=x

3

−x

2

−22x+40

We get the value of y = 0, then that is the possible equation.

When x = -5, y=(−5)

3

−(−5)

2

−22(−4)+40=0

x = 2, y=(2)

3

−(2)

2

−22(2)+40=0

x = 4, y=(4)

3

−(4)

2

−22(4)+40=0

So, the possible equation is y=(2)

3

−(2)

2

−22(2)+40=0.