Advertisements
Advertisements
प्रश्न
If α, β are the zeros of the polynomial p(x) = 4x2 + 3x + 7, then \[\frac{1}{\alpha} + \frac{1}{\beta}\] is equal to
पर्याय
- \[\frac{7}{3}\]
- \[- \frac{7}{3}\]
- \[\frac{3}{7}\]
- \[- \frac{3}{7}\]
उत्तर
Since `alpha` and ß are the zeros of the quadratic polynomial p(x) = 4x2 + 3x + 7,
`alpha + ß = - (text{coefficient of x})/(text{coefficient of } x^2)`
`= (-3)/4`
`alpha ß = (\text{constat term})/(text{coefficient of} x^2)`
`= 7/4`
We have
`= 1/alpha + 1/ ß `
`= (ß + alpha )/(alpha ß )`
`= (-3)/(4/7)`
`= (-3)/4 xx4/7`
`= (-3)/cancel(4)xxcancel(4)/7`
`= (-3)/7`
The value of `1/alpha +1/beta` is `(-3)/7`
Hence, the correct choice is `(d)`
APPEARS IN
संबंधित प्रश्न
Classify the following polynomials as linear, quadratic, cubic and biquadratic polynomials:
`3x-2`
Classify the following polynomials as polynomials in one-variable, two variables etc:
`xy+yx+zx`
Write the standard form of a quadratic polynomial with real coefficients.
If the sum of the zeros of the quadratic polynomial f(x) = kx2 − 3x + 5 is 1, write the value of k.
Write the coefficient of the polynomial p(z) = z5 − 2z2 + 4.
If α, β are the zeros of polynomial f(x) = x2 − p (x + 1) − c, then (α + 1) (β + 1) =
If α, β are the zeros of the polynomial f(x) = x2 − p(x + 1) − c such that (α +1) (β + 1) = 0, then c =
Identify the following expression is polynomial. If not give reason:
`1/x(x + 5)`
Case Study -1
The figure given alongside shows the path of a diver, when she takes a jump from the diving board. Clearly it is a parabola.
Annie was standing on a diving board, 48 feet above the water level. She took a dive into the pool. Her height (in feet) above the water level at any time‘t’ in seconds is given by the polynomial h(t) such that h(t) = -16t2 + 8t + k.
Rita’s height (in feet) above the water level is given by another polynomial p(t) with zeroes -1 and 2. Then p(t) is given by ______.
If a polynomial p(x) is given by p(x) = x2 - 5x + 6, then the value of p(1) + p(4) is ______.
