Question

if a and b are the roots of equation x2-7x+10=0 then write the equation whose roots are 1/a and 1/b​

Answer 1

Answer:

limit as X approaches 1

of x^2-3x+2/x^2-4x+3

Answer 2

Given Quadratic equation → x² - 7x + 10 = 0

Factorise the polynomial by splitting the middle term.

x² - 2x - 5x + 10 = 0

⇒ x(x - 2) - 5(x - 2) = 0

⇒ (x - 5) (x - 2) = 0

⇒ x = 5 or 2

So, the 2 roots of the Equation are 5 and 2

• a = 5
• b = 2

Finding a new Quadratic polynomial with zeroes as ⅕ and ½.

Sum of zeroes

= ⅕ + ½

= 7/10

= 0.7

Product of zeroes

= ⅕ × ½

= ⅒

= 0.1

Quadratic polynomial = x² - (Product of zeroes)x + Sum of zeroes

➝ Quadratic polynomial = x² - (⅕ + ½)x + ⅒

➝ Quadratic polynomial = x² - 0.7x + 0.1

Multiply the whole polynomial by 10

➝ Quadratic polynomial = 10x² - 7x + 1

∴ The required Equation is 10x² - 7x + 1