Question

The one who replies the fastest will get brainliest answer tag but make sure that the answers should be correct

Answer 1

Answer:

Step-by-step explanation:

ax²+bx+c=0

let z1 and z2 be zeroes

z1+z2= -b/a

zz=c/a

then , z1+z2 = -a-c/a

                   =-a/a+ -c/a

                   =1-c/a

Answer 2

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) .