Question

If a and B are roots of the equation x2 + 5x + 5 = 0, then equation whose roots are
a + 1 and b + 1 is
a) x2 + 5x - 5 = 0
b) x2 + 3x + 5 = 0
c) x2 + 3x + 1 = 0
d) None of these

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Answer 1

Answer:

c)  $x^{2} +3x+1$

Step-by-step explanation:

GIVEN:-  $x^{2} +5X+5=0$  with zeroes a & b

TO FIND:-  equation with zeroes a+1 & b+1

               

SOLUTION:-

in the given equation,

let p=1

    q=5

     r=5

$a+b=\frac{-q}{p} \\a+b=\frac{-5}{1} \\a+b= -5$                                     -----------------------------(i)

$ab=\frac{r}{p} \\ab=\frac{5}{1} \\ab=5$                                            ----------------------------(ii)

=_=_=_=_=_=_=_=_=_=_=_=_=_=_=_=_=_=_=_=_=_=_=_=_=_=_=_=_=_=_=_

∴now let us find the sum of the new zeroes

the value of (a+b) & (ab) are taken from (i) & (ii)

$(a+1)+(b+1)\\=a+1+b+1\\=a+b+1+1\\=a+b+2\\=-5+2\\=-3$                                                          

$(a+1)(b+1)\\=ab+a+b+1\\=5+(-5)+1\\=5-5+1\\=0+1\\=1$

now the new equation would have the sum of zeroes as -3

                                                   and the product of zeroes as 1

$x^{2} -(sum of zeroes)x+(product of zeroes)\\ x^{2} -(-3)x+(1)\\x^{2} +3x+1$