Advertisements
Advertisements
प्रश्न
If the graph of quadratic polynomial ax2 + bx + c cuts negative direction of y-axis, then what is the sign of c?
उत्तर
Since graph of quadratic polynomial `f(x)= ax^2 + bx + c`cuts negative direction of y−axis
So put x=0 to find the intersection point on y-axis
` y = 0 + 0 + c +c `
So the point is `(0 , c)`
Now it is given that the quadratic polynomial cuts negative direction of y
So `c < 0`
APPEARS IN
संबंधित प्रश्न
If α, β are the zeros of the polynomial p(x) = 4x2 + 3x + 7, then \[\frac{1}{\alpha} + \frac{1}{\beta}\] is equal to
If zeros of the polynomial f(x) = x3 − 3px2 + qx − r are in A.P., then
Divide. Write the quotient and the remainder.
(8p3 − 4p2) ÷ 2p2
Obtain all the zeroes of the polynomial 2x4 − 5x3 − 11x2 + 20x + 12 when 2 and − 2 are two zeroes of the above polynomial.
Identify the following expression is polynomial. If not give reason:
`1/x^2 + 3x - 4`
Identify the following expression is polynomial. If not give reason:
`sqrt(5)x^2 + sqrt(3)x + sqrt(2)`
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
Case Study -1
The figure given alongside shows the path of a diver, when she takes a jump from the diving board. Clearly it is a parabola.
Annie was standing on a diving board, 48 feet above the water level. She took a dive into the pool. Her height (in feet) above the water level at any time‘t’ in seconds is given by the polynomial h(t) such that h(t) = -16t2 + 8t + k.
At what time will she touch the water in the pool?
Case Study -1
The figure given alongside shows the path of a diver, when she takes a jump from the diving board. Clearly it is a parabola.
Annie was standing on a diving board, 48 feet above the water level. She took a dive into the pool. Her height (in feet) above the water level at any time ‘t’ in seconds is given by the polynomial h(t) such that h(t) = -16t2 + 8t + k.
A polynomial q(t) with sum of zeroes as 1 and the product as -6 is modelling Anu’s height in feet above the water at any time t( in seconds). Then q(t) is given by ______.
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:
