Question

if the zero of the quadratic polynomial x2+(a+1)x+b are 2and -3 then find a and b
​

Answer 1

❥${\red{\underline{\underline{\huge{\mathtt{Question:-}}}}}}$

if the zero of the quadratic polynomial x²+(a+1)x+b are 2 and -3 then find a and b.

❥${\red{\underline{\underline{\huge{\mathtt{Solution:-}}}}}}$

${\green{\bold{\ Equation→}}}$

x²+(a+1)x+b = 0

★ In 1st case , putting x = 2 in the equation ★

x²+(a+1)x+b = 0

→ 2² + (a+1)×2 + b = 0

→ 4 + 2a+2 + b = 0

→ 2a + b = -6....................(i)

★ In 2nd case, putting x= -3 in the equation★

x²+(a+1)x+b = 0

→(-3)² + (a+1) ×(-3) + b = 0

→ 9 - 3a - 3 +b = 0

→ - 3a +b = -6

→ 3a - b = 6................(ii)

${\blue{\bold{By\: elimination:-}}}$

2a+b = -6

3a - b = 6

______________

5a = 0

→ a = 0

✞putting a= 0 in (i) no. equation✞

2a + b = -6

→ 2×0 + b = -6

→ b = -6

❥${\red{\underline{\underline{\huge{\mathtt{Answer:-}}}}}}$

a = 0

b = -6

Answer 2

$\huge \mathfrak{Answer:-}$

$\implies$a = 0

$\implies$b = -6

$\large\underline\mathrm{Given:-}$

• the zero of the quadratic polynomial x²+(a + 1)x + b.

$\large\underline\mathrm{To \: find}$

• find a and b.

$\large\underline\mathrm{Solution}$

• x²+(a + 1)x + b

$\large\underline\mathrm{Putting \: x \: = \: 2 \: in \: the \: equation:-}$

$\implies$ x²+(a + 1)x + b

$\implies$ 2²+(a + 1)² + b = 0

$\implies$ 4 + 2a + 2 + b = 0

$\implies$ 2a + b = -6_____(1)

putting x = -3 in the equation.

$\implies$ x²+(a + 1)x + b

$\implies$ -3²+(a + 1)-3 + b = 0

$\implies$ 9 - 3a - 3 + b = 0

$\implies$ 3a + b = -6_____(2)

By Elimination

2a + b = -6

3a + b = -6

____________

5a = 0

$\implies$ a = 0

putting a = 0 in equation (1).

$\implies$ 2a + b = -6

$\implies$ 2(0) + b = -6

$\implies$ 0 + b =-6

hence,

$\implies$a = 0

$\implies$b = -6

$\large\underline\mathrm{Hope \: it \: helps \: you \: plz \: mark \: me \: brainlist}$