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The one who replies the fastest will get brainliest answer tag but make sure that the answers should be correct
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Question:
If p(x) = ax² + bx + c and a + c = b , then find one of its zeros .
Answer:
x = -1
Note:
∆ The general form of a quadratic polynomial is given as ; p(x) = ax² + bx + c .
∆ Zeros of a polynomial p(x) are the possible values of x for which the p(x) become zero.
∆ To find the zeros of polynomial p(x) , operate on p(x) = 0.
∆ The maximum number of zeros of a polynomial is equal to its degree.
∆ A quadratic polynomial will have at most two zero , as its degree is 2 .
∆ If A and B are the zeros of the quadratic polynomial p(x) = ax² + bx + c , then ;
• Sum of zeros,(A+B) = - b/a
• Product of zeros,(A•B) = c/a
∆ If A and B are given zeros of a quadratic polynomial p(x)., then p(x) will be given as ;
p(x) = x² - (A+B)x + A•B
Solution:
The given polynomial is p(x) = ax² + bx + c
Also , it is given that b = a + c .
Now,
Substituting the value b = a + c in the given polynomial, we have ;
p(x) = ax² + (a+c)x + c
Now ,
In order to find the zeros of the given polynomial , let's operate on p(x) = 0.
Thus,
=> ax² + (a+c)x + c = 0
=> ax² + ax + cx + c = 0
=> ax(x+1) + c(x+1) = 0
=> (x+1)(ax+c) = 0
=> x+1 = 0 or ax+c = 0
=> x = -1 or x = -c/a
Hence,
If p(x) = ax² + bx + c and b = a+c , then x = -1 will always be a zero of polynomial p(x) .