Question

If 1 is a common root of the quadratic equation ax² + ax+3= 0 and the quadratic equation ax² + ax + b= 0 ,then find a and b.​

Answer 1

Answer:

n ax² + ax+3= 0 and the quadratic equation ax² + ax + b= 0 ,then find a and b.​

Step-by-step explanation:

n ax² + ax+3= 0 and the n ax² + ax+3= 0 and the quadratic equation ax² + ax + b= 0 ,then find a and b.​ ax² + ax+3= 0 and the quadratic equation ax² + ax + b= 0 ,then find a and b.​ic equation ax² + ax + b= 0 ,then find a and b.​n ax² + ax+3= 0 and the quadratic equation ax² + ax + b= 0 ,then find a and b.​

Answer 2

$\large\underline\mathfrak\red{Given \: :- }$

• x =1 is the common roots given quadratic equation are ax² + ax + 3 = 0 and x² + x + b =0.

$\large\underline\mathfrak\red{To \: find \: :- }$

• a and b

$\large\underline\mathfrak\red{Solution \: :- }$

We know that,

x =1 is the common roots given quadratic equation are ax² + ax + 3 = 0 and x² + x + b =0.

Here,

ax² + ax + 3 = 0 ...(1)

x² + x + b =0 ...(2)

Putting the value of x = 1 in equation (1)

$\sf\implies{ax {}^{2} + ax + 3 = 0} \: \: \: \: \: \: \: \\ \sf\implies{a(1) {}^{2} + a(1) + 3 = 0} \\ \sf\implies{a + a + 3 = 0} \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \sf\implies{2a = - 3} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \sf\implies{a = \frac{ - 3}{2} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

Now,

Putting value x = 1 in equation (2)

$\sf\implies{x {}^{2} + x + b = 0 } \\ \sf\implies{1 {}^{2} + 1 + b = 0 } \\ \sf\implies{1 + 1 + b = 0} \: \\ \sf\implies{2 + b = 0} \: \: \: \: \: \: \: \: \: \\ \sf\implies{b = - 2} \: \: \: \: \: \: \: \: \: \: \: \: \:$

${\underline{\boxed{\sf{\red{a = \frac{ - 3}{2} }}}}}$

${\underline{\boxed{\sf{\red{b = -2}}}}}$

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If you want ab

$\sf\implies{ab = \frac{ - 3}{2} \times - 2 } \\ \sf\implies{ab = - 3 \times - 1} \\ \sf\implies{ab = 3} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

${\underline{\boxed{\sf{\red{ab = 3 }}}}}$

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