Q) Find X in terms of a b, and c: , X ≠ a, b, c Ans: Given equation is: ∴ ∴ [a (X – b) + b (X – a)] (X – c) = 2 c (X – a) (X – b) ∴ (a X – a b + […]
Find x in terms of a b, and c: a/(x – a) + b/(x – b) = 2 c/(x – c), x ≠ a, b, c Read More »
polynomials
Q) Swimming Pool : The volume of water in a rectangular, in-ground, swimming pool is given by V (x)= x3 + 11 x2 + 24x, where V (x) is the volume in cubic feet when the water is x ft high. (i) Find the dimension of base of pool. (ii) Use the remainder theorem to
The volume of water in a rectangular, in-ground, swimming pool is given by V (x)= Read More »
Q) Find the value of ‘k’ for which the quadratic equation (k + 1) y2 – 6 (k + 1) y + 3 (k + 9) = 0, k ≠ – 1 has real and equal roots. [CBSE 2024 – Series 5 – Set 1] Ans: Given quadratic equation is: (k
Find the value of k for which the quadratic equation (k + 1) y2 – 6(k +1) y + 3(k +9)= 0 Read More »
Q) An asana is a body posture, originally and still a general term for a sitting meditation pose, and later extended in hatha yoga and modern yoga as exercise, to any type of pose or position, adding reclining, standing, inverted, twisting, and balancing poses. In the figure, one can observe that poses can be related
Q) 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. 1. In the standard form of quadratic polynomial, a x2 + b x + c, a, b
Q. Divide the polynomial x3 – 3 x2 + 5 x – 3 by x2 – 2 Ans: To divide the given polynomial, we can write the function as: = = = = = = = = = = = = Therefore, When we divide X3 – 3 X2 + 5 X – 3 by X2
Divide the polynomial x³ – 3x² + 5x – 3 by x² – 2 Read More »
Q. Solve the quadratic equation: 2 X^2 – 7 X + 3 = 0 Ans: Given equation is: 2 X ^2 – 7 X + 3 = 0 ∴ 2 X ^2 – 6 X – X + 3 = 0 ∴ 2 X (X – 3) – 1 (X – 3) = 0 ∴
Q) Find the value of ‘k’ for which the quadratic equation (k + 1) x 2 – 2 (3 k + 1) x + (8 k + 1) = 0 has real and equal roots. [CBSE 2024 – Series 4 – Set 2] Ans: Given quadratic equation is: (k + 1) x
Q) Find the zeroes of the polynomial 4×2 + 4x – 3 and verify the relationship between zeroes and coefficients of the polynomial. Ans: In the given polynomial equation, to find zeroes, we will start with f(x) = 0 Therefore, 4 x2 + 4 x – 3 = 0 Step 1: Let’s start calculating the
Q) If 𝛼, β are zeroes of quadratic polynomial x2 + x – 2, find the value of Ans: In the given polynomial equation f(x), to find zeroes, we will start with f(x) = 0 Therefore, x2 + x – 2 = 0 Step 1: Given that the roots of the polynomial are α and
If 𝛼, β are zeroes of quadratic polynomial x2 + x – 2, find the value of 𝛼/𝛽 + 𝛽 /𝛼. Read More »