Advertisements
Advertisements
प्रश्न
Figure 2.23 show the graph of the polynomial f(x) = ax2 + bx + c for which
पर्याय
a < 0, b > 0 and c > 0
a < 0, b < 0 and c > 0
a < 0, b < 0 and c < 0
a > 0, b > 0 and c < 0
उत्तर
Clearly, f(x) = ax2 + bx + c represent a parabola opening downwards. Therefore, `a < 0`
` y= ax^2 + bx + c ` cuts y-axis at P which lies on `OY`. Putting x = 0 in ` y = ax^2 + bx + c `, we get y =c. So the coordinates P are `(0,c)`. Clearly, P lies on `(OY)`. Therefore `c > 0`
The vertex `(-b)/(2a), (-D)/(4a)` of the parabola is in the second quadrant. Therefore `-b /(2a)`, `b < 0`
Therefore `a < 0,b>0` and `c > 0`
Hence, the correct choice is `(b)`
APPEARS IN
संबंधित प्रश्न
Define degree of a polynomial.
The graph of the polynomial f(x) = ax2 + bx + c is as shown in Fig. 2.20. Write the value of b2 − 4ac and the number of real zeros of f(x).
If f(x) = x3 + x2 − ax + b is divisible by x2 − x write the value of a and b.
If f(x) is a polynomial such that f(a) f(b) < 0, then what is the number of zeros lying between a and b?
If α, β are the zeros of the polynomial p(x) = 4x2 + 3x + 7, then \[\frac{1}{\alpha} + \frac{1}{\beta}\] is equal to
State whether the given algebraic expression are polynomial? Justify.
`x^2 + 7x + 9`
Divide. Write the quotient and the remainder.
(21x4 − 14x2 + 7x) ÷ 7x3
Identify the following expression is polynomial. If not give reason:
`"m"^2 - root(3)("m") + 7"m" - 10`
The below picture are few natural examples of parabolic shape which is represented by a quadratic polynomial. A parabolic arch is an arch in the shape of a parabola. In structures, their curve represents an efficient method of load, and so can be found in bridges and in architecture in a variety of forms.
If the roots of the quadratic polynomial are equal, where the discriminant D = d2 – 4ac, then:
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 graph of parabola opens upwards, if:
