Question

if (x+a) is a factor of p (x) then p (-a)​

Answer 1

Answer:

10th

Maths

Polynomials

Relationship between Zeroes and Coefficients of a Polynomial

If x + a is a factor of x2 ...

MATHS

If x+a is a factor of x

2

+px+q and x

2

+mx+n, show that a=

m−p

n−q

.

HARD

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ANSWER

Given :

(x+a) is a factor of x

2

+px+q and x

2

+mx+n

then using the factor theorem which says that the polynomial f(x0 has a factor (x−k) if and only if f(k)=0

We have

(−a)

2

+p(−a)+q=0⟶(1)

⇒a

2

−ap+q=0⟶(2)

and

(−a)

2

+m(−a)+n=0⟶(3)

⇒a

2

−ma+n=0⟶(4)

Subtracting (2) & (4) we get

−ap+am+q−n=0

⇒+a(m−p)=n−q

⇒a=

m−p

n−q

Hence, proved

Step-by-step explanation:

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