Solving a Quadratic Equation by Factorization Method
If the zeros ...
Question
If the zeros of the polynomial x3−3x2+x+1 are a−b,a,a+b, find a and b.
A
a=1 and b=±√2
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
a=±1 and b=±√2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
a=2 and b=±1
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
a=−1 and b=±√2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution
The correct option is Aa=1 and b=±√2 The given polynomial is x3−3x2+x+1 As (a−b),a and (a+b) are the zeros of the given polynomial ⇒(a−b)3−3(a−b)2+(a−b)+1=0 .....(1) ⇒a3−3a2+a+1=0 ....(2) and (a+b)3−3(a+b)2+(a+b)+1=0 .....(3) Putting a=1 in equation (2), we get 1−3+1+1=0 or 0=0 ⇒ (2) is satisfied, when a=1 ∴1 is a zero of the given polynomial Putting a=1 in (1), we get (1−b)3−3(1−b)2+(1−b)+1=0 ⇒1−b3−3b+3b2−3(1−2b+b2)+1−b+1=0 ⇒3−4b+3b2−b3−3+6b−3b2=0 ⇒−b3+2b=0 ⇒−b(b2−2)=0 Either b=0 or b2−2=0 But b can not be zero