Question

relationship between zeroes and cofficient. root 5+2;root 2-3​

Answer 1

Answer:

quadratic polynomial is given, 2√3x² - 5x + √3 .

2√3x² - 5x + √3 = 0

or, 2√3x² - 2x - 3x + √3 = 0

or, 2√3x² - 2x - √3 × √3 × x + √3 = 0

or, 2x(√3x - 1) - √3(√3x - 1) = 0

or, (2x - √3)(√3x - 1) = 0

or, x = √3/2 and 1/√3

verification : sum of roots = -b/a

LHS = sum of roots = √3/2 + 1/√3 = 5/2√3

RHS = -b/a = -(-5)/2√3 = 5/2√3

LHS = RHS

again, product of roots = c/a

LHS = √3/2 × 1/√3 = 1/2

RHS = √3/2√3 = 1/2

LHS = RHS

hence verified.

Step-by-step explanation:

Answer 2

Step-by-step explanation:

Zeroes of a quadratic equation is the factors of the polynomial.

Coefficients are numerical or constant quantity placed before and multiplying the variable in an algebraic expression.

Relation for Coefficients with roots in a quadratic equation is

α + β = -b/a

αβ = c/a

$\sqrt{5 + 2} = \sqrt{7} = 2.645.......$

$\sqrt{2 - 3} = \sqrt{ - 1}$

√-1 cannot be obtained, so in Mathematics, √-1 is expressed as "i" ( Iota )

To know more, Have a look at Complex Numbers & Quadratic Equations ( Chapter 5, +1 Mathematics)