CBSE Class 10 Maths (Basic) 2023 · Paper 430/5/1 · Question 36

Polynomials 4 marks Hard

Rainbow is an arch of colours that is visible in the sky after rain or when water droplets are present in the atmosphere. The colours of the rainbow are generally, red, orange, yellow, green, blue, indigo and violet. Each colour of the rainbow makes a parabola. We know that any quadratic polynomial

p (x) = a x^{2} + b x + c (a \neq = 0)

represents a parabola on the graph paper. Based on the above, answer the following questions :

Downward-opening parabola crossing the x-axis at two points

(i)The graph of a rainbow $y = f (x)$ is shown in the figure. Write the number of zeroes of the curve.[1]
(ii)If the graph of a rainbow does not intersect the x-axis but intersects the y-axis at one point, then how many zeroes will it have ?[1]
(iii)(a)If a rainbow is represented by the quadratic polynomial $p (x) = x^{2} + (a + 1) x + b$ , whose zeroes are 2 and $- 3$ , find the value of $a$ and $b$ .[2]
(iii)(b) ORThe polynomial $x^{2} - 2 x - (7 p + 3)$ represents a rainbow. If $- 4$ is a zero of it, find the value of $p$ .[2]

Answer

(i) 2 zeroes; (ii) 0 zeroes; (iii)(a)

a = 0, b = - 6

; (iii)(b)

p = 3

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CBSE Class 10 Maths (Basic) 2023 · Paper 430/5/1 · Question 36

Answer

From the board paper

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