Question

Q21. Find the zeroes of the quadratic polynomials p(x) and verify the relationship between the zeros and the coefficients. p(x)= 3x² -x -4​

Answer 1

Answer:

Given quadratic equation:

• 3x² - x - 4

Solving the quadratic equation by splitting the middle term we get,

→ 3x² + 3x - 4x - 4 = 0

→ 3x ( x + 1 ) - 4 ( x + 1 ) = 0

→ ( 3x - 4 ) ( x + 1 ) = 0

→ 3x - 4 = 0 ⇒ x = 4/3

→ x + 1 = 0 ⇒ x = -1

Relationship between zeros and coefficients:

• Sum of zeros = - ( coefficient of x ) / ( coefficient of x² )
• Product of zeros = ( constant term ) / ( coefficient of x² )

According to the given equation,

→ Sum of zeros = 4/3 - 1 = 1/3

→ Product of zeros = 4/3 × -1 = -4/3

Now comparing it with the relationship we get:

→ Sum of zeros = - ( - 1 ) / 3 = 1/3

→ Product of zeros = ( -4 ) / 3 = -4/3

Hence both of them tally each other.

LHS = RHS

Hence verified!!

Answer 2

Answer:

$\bf \huge \color{fuchsia} {Given:-}$

3x² - x - 4

Solving the quadratic equation by splitting the middle term we get,

$\color{purple} {\bf \huge \looparrowright}$ 3x² + 3x - 4x - 4 = 0

$\color{purple} {\bf \huge \looparrowright}$ 3x ( x + 1 ) - 4 ( x + 1 ) = 0

$\color{purple} {\bf \huge \looparrowright}$ ( 3x - 4 ) ( x + 1 ) = 0

$\color{purple} {\bf \huge \looparrowright}$ 3x - 4 = 0 ⇒ x = 4/3

$\color{purple} {\bf \huge \looparrowright}$ x + 1 = 0 ⇒ x = -1

$\color{purple} {\bf \huge \looparrowright}$Relationship between zeros and coefficients:

$\color{purple} {\bf \huge \looparrowright}$ Sum of zeros = - ( coefficient of x ) / ( coefficient of x² )

$\color{purple} {\bf \huge \looparrowright}$Product of zeros = ( constant term ) / ( coefficient of x² )

$\color{purple} {\bf \huge \looparrowright}$ Sum of zeros = 4/3 - 1 = 1/3

$\color{purple} {\bf \huge \looparrowright}$Product of zeros = 4/3 × -1 = -4/3

$\color{purple} {\bf \huge \looparrowright}$Now comparing ,

$\color{purple} {\bf \huge \looparrowright}$ Sum of zeros = - ( - 1 ) / 3 = 1/3

$\color{purple} {\bf \huge \looparrowright}$ Product of zeros = ( -4 ) / 3

= -4/3

$\color{purple} {\bf \huge \looparrowright}$Hence both of them tally each other.

$\color{purple} {\bf \huge \looparrowright}$LHS = RHS

$\bf \huge \color{red} {Verified\checkmark}$

Step-by-step explanation:

i hope it helps uh.