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प्रश्न
State division algorithm for polynomials.
उत्तर
If f (x) and g (x) are any two polynomials with `g (x ) ≠ 0 `then we can always find polynomials ` q(x)` and `r (x)` such that `f (x)= q(x)g(x)+ r(x)`, where `r (x) = 0` or degree r(x) degree g(x)
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संबंधित प्रश्न
Classify the following polynomials as linear, quadratic, cubic and biquadratic polynomials:
`2x+x^2`
Write the family of quadratic polynomials having \[- \frac{1}{4}\] and 1 as its zeros.
In Q. No. 15, write the sign of c.
The graph of a polynomial f(x) is as shown in Fig. 2.21. Write 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 the graph of quadratic polynomial ax2 + bx + c cuts negative direction of y-axis, then what is the sign of c?
Divide. Write the quotient and the remainder.
(5x3 − 3x2) ÷ x2
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?
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 α and `1/α` are the zeroes of the quadratic 2x2 − x + 8k, polynomial 2 then k is:
Degree of the polynomial 4x4 + 0x3 + 0x5 + 5x + 7 is ______.
