9. If the zeroes of the quadratic polynomial ax2+bx+c are additive inverse to each other
then which of the following condition is true
(A)c=o
(B) b = 0
(C) c= a
(D) a b
Answers
Answer:
General Polynomial
If we have a general polynomial like this:
f(x) = axn + bxn-1 + cxn-2 + ... + z
Then:
Adding the roots gives −b/a
Multiplying the roots gives:
z/a (for even degree polynomials like quadratics)
−z/a (for odd degree polynomials like cubics)
Which can sometimes help us solve things.
How does this magic work? Let's find out ...
Factors
We can take a polynomial, such as:
f(x) = axn + bxn-1 + cxn-2 + ... + z
And then factor it like this:
f(x) = a(x−p)(x−q)(x−r)...
Then p, q, r, etc are the roots (where the polynomial equals zero)
Quadratic
Let's try this with a Quadratic (where the variable's biggest exponent is 2):
ax2 + bx + c
When the roots are p and q, the same quadratic becomes:
a(x−p)(x−q)
Is there a relationship between a,b,c and p,q ?
Let's expand a(x−p)(x−q):
a(x−p)(x−q)
= a( x2 − px − qx + pq )
= ax2 − a(p+q)x + apq
Now let us compare:
Quadratic: ax2 +bx +c
Expanded Factors: ax2 −a(p+q)x +apq
We can now see that −a(p+q)x = bx, so:
−a(p+q) = b
p+q = −b/a
And apq = c, so:
pq = c/a
And we get this result:
Adding the roots gives −b/a
Multiplying the roots gives c/a
This can help us answer questions.
Example: What is an equation whose roots are 5 + √2 and 5 − √2
The sum of the roots is (5 + √2) + (5 − √2) = 10
The product of the roots is (5 + √2) (5 − √2) = 25 − 2 = 23
And we want an equation like:
ax2 + bx + c = 0
When a=1 we can work out that:
Sum of the roots = −b/a = -b
Product of the roots = c/a = c
Which gives us this result
x2 − (sum of the roots)x + (product of the roots) = 0
The sum of the roots is 10, and product of the roots is 23, so we get:
x2 − 10x + 23 = 0
And here is its plot:
Step-by-step explanation:
option - b...
hope it will help you... please mark it as brainliest
