If (x – 6) is a factor of x^3 + ax^2 + bx – b = 0 and a – b = 7, find the values of a and b.

Solution: Since the ordered pairs are equal, the corresponding elements are equal. Therefore x + 1 = 3 and y – 2 = 1. Solving we get x = 2 and y...

Let take the number be  600851475143, so to find the largest prime factor run the following code Result : 6857 <?php $max = 600851475143; $l_num = 0; for ($j = floor(sqrt($max)) / 2; $j >= 2;...

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...

A = {9, 10, 11, 12, 13} f: A → N is defined as f(n) = The highest prime factor of n  Prime factor of 9 = 3  Prime factors of 10...

(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 ≤...

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

A = {9, 10, 11, 12, 13} f: A → N is defined as f(n) = The highest prime factor of n Prime factor of 9 = 3 Prime factors of 10 =...

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