Advertisements
Advertisements
प्रश्न
If α, β are the zeros of the polynomial f(x) = x2 − p(x + 1) − c such that (α +1) (β + 1) = 0, then c =
पर्याय
1
0
-1
2
उत्तर
Since `alpha` and `beta` are the zeros of quadratic polynomial
f(x) = x2 − p(x + 1) − c
`f(x)= x^2 - px -p-c`
`alpha + ß = - (text{coefficient of x})/(text{coefficient of } x^2)`
`= -(-p/1)`
`= p`
`alphabeta= (\text{Coefficient of x})/(\text{Coefficient of}x^2)`
`= (-p-c)/1`
`= -p-c`
We have
`0 = (alpha + 1)(beta+1)`
`0=alpha beta + (alpha +beta)+1`
`0 = - cancel(p)-c + cancel(p) +1`
`0 = -c +1`
The value of c is 1.
Hence, the correct alternative is `(a)`
APPEARS IN
संबंधित प्रश्न
In Q. No. 15, write the sign of c.
If α, β are the zeros of the polynomial 2y2 + 7y + 5, write the value of α + β + αβ.
If a quadratic polynomial f(x) is factorizable into linear distinct factors, then what is the total number of real and distinct zeros of f(x)?
State whether the given algebraic expression is polynomial? Justify.
10
Divide. Write the quotient and the remainder.
(−48p4) ÷ (−9p2)
Divide. Write the quotient and the remainder.
40m5 ÷ 30m3
Let the polynomials be
(A) −13q5 + 4q2 + 12q
(B) (x2 + 4)(x2 + 9)
(C) 4q8 – q6 + q2
(D) `– 5/7 y^12 + y^3 + y^5`
Then ascending order of their degree is
The number of polynomials having zeroes as 4 and 7 is ______.
Basketball and soccer are played with a spherical ball. Even though an athlete dribbles the ball in both sports, a basketball player uses his hands and a soccer player uses his feet. Usually, soccer is played outdoors on a large field and basketball is played indoor on a court made out of wood. The projectile (path traced) of soccer ball and basketball are in the form of parabola representing quadratic polynomial.
The shape of the path traced shown is:
The degree of the sum of two polynomials each of degree 5 is always 5.
