If (x + 1, y – 2) = (3,1), find the values of x and y.

Solution: From the given polynomial p(x), α + β = −4/r, and αβ = −4/r………. (1) Since,(α + β)2 = α2 + β2 + 2αβ Given,   α2 + β2 = 24 and from equation (1). Therefore,  (−4/r)2=24+(2×4)/r 16/r2=24+(2×4)/r 16 = 24 r2 + 8r 3r2 + r – 2 = 0 3r2 + 3r...

Solution: If (x - 6) is a factor then f(6) = 0, that is  6³ + a6² + b(6) - b = 0  216 + 36a + 6b - b = 0  36a +...

Cl2 < MnO4 _ < Ce4+ 

Stability of an ionic compound depends on its lattice energy. More the lattice energy of a compound, more stable it will be. Lattice energy is directly proportional to the charge carried...

(iii) The given function is f(x) = − (x − 1)2 + 10. It can be observed that (x − 1)2 ≥ 0 for every x ∈ R. Therefore, f(x) = −...

(iv) The given function is g(x) = x3 + 1. Hence, function g neither has a maximum value nor a minimum value.

(iii) h(x) = sin2x + 5 We know that − 1 ≤ sin 2x ≤ 1. ∴ − 1 + 5 ≤ sin 2x + 5 ≤ 1 + 5 ∴ 4 ≤...

(iv)f(x) = |sin4+3| We know that −1 ≤ sin 4x ≤ 1. ∴ 2 ≤ sin 4x + 3 ≤ 4 ∴ 2 ≤ |sin4+3| ≤ 4 Hence, the maximum and minimum values of...

The following combinations can be obtained: (i) The individual resistances: 2‎Ω,3‎Ω,6‎Ω (ii) All in series: 11‎Ω (iii) All in parallel: 11‎Ω (iv) Three different possible mixed grouping of resistors:4‎Ω,9/2‎Ω36/5‎Ω

Answer is..... a=3,b=-6