Explanation

Equation 2x² − 3x − 2 = 0  

Break -3x into -4x + 1x because 2 × -2 = -4 and -4 + 1 = -3  

So 2x² − 4x + 1x − 2 = 0  

Take 2x common from first two terms → 2x(x − 2)  

Take 1 common from last two terms → 1(x − 2)  

Now we get (2x + 1)(x − 2) = 0  

If two things multiply to 0, one of them is 0  

So 2x + 1 = 0 gives x = -1/2  

And x − 2 = 0 gives x = 2

Final: x = 2, −1/2

Last verified on 20-06-2026

Explanation

Matrix multiplication is Associative → (AB)C = A(BC)

Last verified on 17-06-2026

Explanation

The identity matrix has all diagonal elements as 1 and is full rank.

All its rows/columns are linearly independent.

Therefore, a 3 × 3 identity matrix has rank 3.

Last verified on 17-06-2026

Explanation

2y − x + 8 = 0

2y = x − 8

y = (1/2)x − 4

Slope (m) = coefficient of x = 1/2

Last verified on 17-06-2026

Explanation

Given:

f(x) = 5x + x² − 1

g(x) = 2x + 5

Step 1: Find g(4)

g(4) = 2(4) + 5 = 8 + 5 = 13

Step 2: Find f(g(4)) = f(13)

f(13) = 5(13) + 13² − 1

= 65 + 169 − 1

= 233

Last verified on 17-06-2026