Explanation

For quadratic ax² + bx + c = 0:  

Sum of roots = -b/a  

Product of roots = c/a  

Take a = 1, then:  

-b = sum = -2 → b = 2  

c = product = 3  

So equation: x² + 2x + 3 = 0

Last verified on 23-06-2026

Explanation

Inverse proportion: y ∝ 1/x, so y × x = constant

Given: 10 × 2 = 20

So when x = 5 ⇒ y = 20 ÷ 5 = 4

Last verified on 23-06-2026

Explanation

Let the 3-digit number be abc = 100a + 10b + c  

Reversed = cba = 100c + 10b + a  

Given: reversed - original = 297  

(100c + 10b + a) - (100a + 10b + c) = 297  

99c - 99a = 297 → 99(c - a) = 297 → c - a = 3  

Also given: a + c = 7  

Solve:  

a + c = 7  

c - a = 3  

Add both: 2c = 10 → c = 5  

Then a = 7 - 5 = 2  

Product of first and third digits = a × c = 2 × 5 = 10.

Last verified on 23-06-2026

Explanation

2x² + 5x − 12 = 0

Factor form: (2x − 3)(x + 4) = 0

So, x = 3/2 or x = −4

Last verified on 22-06-2026

Explanation

Odd function: F(-x) = -F(x) → F(x) + F(-x) = 0

Even function: F(-x) = F(x) → F(x) + F(-x) = 2F(x)

Here we have F(x) + F(-x) = 6, a constant

That means the function is symmetric about y = 3

So we call it constant symmetric form.

Last verified on 21-06-2026

Explanation

When a value of x is given, we replace x in the polynomial and simplify to get the result.

This is called evaluation of a polynomial.

Last verified on 21-06-2026

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