Explanation

x² - 3x + 2 = 0  

This splits as (x - 1)(x - 2) = 0  

So the roots are x = 1 and x = 2

If we multiply each root by 2:  

1 × 2 = 2  

2 × 2 = 4  

New roots are 2 and 4

To make the equation with roots 2 and 4:  

(x - 2)(x - 4) = 0  

x² - 4x - 2x + 8 = 0  

x² - 6x + 8 = 0

Last verified on 09-05-2026

Explanation

Factors are (x - m)(x - n) = x² - (m + n)x + mn  

So m + n = p and mn = 30  

Numbers that multiply to 30 and differ by 1: 5 and 6, or -5 and -6  

So p = 5 + 6 = 11 or p = -5 + (-6) = -11

Last verified on 09-05-2026

Explanation

(a + bi)(a - bi) = a² - (bi)² = a² - b²i²

Since i² = -1, this becomes a² - b²(-1) = a² + b²

Given (a + bi)(a - bi) = 29, so a² + b² = 29

Last verified on 09-05-2026

Explanation

a² + b² = 50  

5² + b² = 50  

25 + b² = 50  

b² = 25  

b = ±5  

Last verified on 08-05-2026

Explanation

Problem: (5x + 3)/(x(x + 1))

Step 1: Set up  

(5x + 3)/(x(x + 1)) = A/x + B/(x + 1)

Step 2: Find A  

Put x = 0 in (5x + 3)/(x + 1)  

(5_0 + 3)/(0 + 1) = 3/1 = 3  

So A = 3

Step 3: Find B  

Put x = -1 in (5x + 3)/x  

(5_-1 + 3)/(-1) = (-5 + 3)/(-1) = -2/-1 = 2  

So B = 2

Answer: 3/x + 2/(x + 1)

Last verified on 08-05-2026

Explanation

f(2) = 2² - 2 = 4 - 2 = 2  

f(1) = 1² - 1 = 1 - 1 = 0  

f(2) - f(1) = 2 - 0 = 2  

Last verified on 08-05-2026

Explanation

y ∝ x means y = kx  

Find k: 10 = k(2) → k = 5  

So y = 5x  

When x = 7: y = 5(7) = 35  

Last verified on 08-05-2026

Explanation

2(x + 1) = x + 7  

2x + 2 = x + 7  

2x - x = 7 - 2  

x = 5  

Last verified on 08-05-2026

Explanation

x² - 6x + 8 = 0 → (x - 2)(x - 4) = 0  

Roots: 2 and 4  

Increase each by 1: new roots are 3 and 5  

New equation: (x - 3)(x - 5) = x² - 8x + 15 = 0  

Last verified on 08-05-2026

Explanation

Let the roots be r and r + 2.  

Product of roots = 24  

r(r + 2) = 24  

r² + 2r - 24 = 0  

(r + 6)(r - 4) = 0  

r = 4 or r = -6  

Sum of roots = p  

If r = 4: roots are 4 and 6 → p = 4 + 6 = 10  

If r = -6: roots are -6 and -4 → p = -6 + (-4) = -10  

Last verified on 08-05-2026