Download App

Polynomials — Maths STD 9 — Question

Gujarat BoardEnglish MediumSTD 9MathsPolynomials1 Mark
MCQ
If x2 - 1 is a factor of ax4 +bx 3 + cx2 + dx + e, then.
  • A
    a + c + e = b + d
  • B
    a + b + e = c + d
  • C
    b + c + d = a + e
  • D
    a + b + c = d + e
✓

Answer

  1. a + c + e = b + d
    Solution:
    As (x2 - 1) Is a factor of polynomial
    f(x2) = ax4 + bx3 + cx2 + dx + e
    Therefore,
    f(x) = 0
    And,
    f(1) = 0
    a(1)4 + b(1)3 + c(1)2 + d(1) + e = 0
    ⇒ a + b + c + d + e = 0
    And,
    f(-1) = 0
    a(-1)4 + b(-1)3 + c(-1)2 + d(-1) + e = 0
    a - b - c - d + e = 0
    Hence, a + c + e = b + d

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q" from Polynomials→Polynomials — all question types→Maths STD 9 question papers→Gujarat Board STD 9 question papers→Gujarat Board question paper generator→

Similar questions

The remainder when x31 - 31 is divided by x + 1 is:
→
→
If $3 x=a+b+c$, then the value of $(x-a)^3+(x-b)^3+(x-c)^3-3(x-a)(x-b)(x-c)$, is
→
The area of the triangle formed by the points P(0,1), Q(0, 5) and R(3, 4) is:
→
Write the correct answer in the following:
Point (-3, 5) lies in the:
→
In the given figure, chords AB and CD intersect at P. If $\angle\text{DPB}=88^\circ$ and $\angle\text{DAP}=46^\circ,$ then the measure of $\angle\text{ABC}$ is:
→
If a - b = -8 and ab = -12, then a3 - b3 =
→
If x + y + z = 9 and xy + yz + zx = 23, the value of (x3 + y3 + z3 - 3xyz) = ?
  1. 108
  2. 207
  3. 669
  4. 729
→
If (3x - 1)7 = a7x7 + a6x6 + a5x5 + ___ + a1x + a0, then a7 + a6 + a5 + ____ + a1 + a0 =
→
In Fig, if AC is bisector of $\angle\text{BAD}$ such that AB = 3cm and AC = 5cm, then CD =
→